Succeed at Options Even If You Don't Know Where to Start
4.8 (13 ratings)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
89 students enrolled

Succeed at Options Even If You Don't Know Where to Start

How 20K Turns into 1.2M in 10 Years
Highest Rated
4.8 (13 ratings)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
89 students enrolled
Created by Scott Brown
Last updated 4/2017
English [Auto-generated]
Current price: $139.99 Original price: $199.99 Discount: 30% off
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This course includes
  • 1.5 hours on-demand video
  • 1 article
  • 1 downloadable resource
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion
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What you'll learn
  • Identify the best and avoid the worst option investing strategies.
  • Master the differences between stock and futures options.
  • Employ the pricing and mechanics of options.
  • English reading and listening comprehension useful as well as an understanding of rudimentary math.

The stock option business is as tough as crab fishing the Alaskan waters. But returns can be eye-popping if you develop an edge. Cornwall Capital, has extracted 51% annually from the stock market over the last decade blossoming every 20k invested into 1.2 million.

Here are a couple of unbreakable rules

Make sure all these items are present…

First, let me clarify something: Many people lose money trading stock options. Here are the rules academic research reveals to be the best in trading options:

Rule #1

Buy in-the-money calls on a couple of the strongest stocks you can identify trading across the NYSE, AMEX, and NASDAQ. Go out at least 6 months. 

Rule #2

Utilize anomalies of momentum, price impact, and post earnings announcement drift (PEAD) to add a few percentage points above the 9 to 10% geometric expected return of stocks. 

Rule #3

Focus on identifying the elephant in the room.  These are captain-obvious-after-the-fact business franchises that make headlines and rapidly become one or two-word household names. 

  • Amazon.
  • Google.
  • Apple.
  • Facebook.
  • Fiat-Chrysler.
  • Netflix

These new, fast rising firms attract the most capital in the market.  These behemoths are partially owned by activist investors who batter executives into doing the right thing for you. 

Rule #4

Focus most on controlling your downside and the rest will follow.  Limit order strops only partially help.  You must be on your computer screen throughout the day to trade calls. 

Rule #5

Focus on options where (1) implied volatility is low (2) the share price is rising and (3) the indexes are bullish. This is when you will initiate your best trades. 

How a 20K Investment Turns into 1.2 M in 10 Years

This course is for anybody interested in options. 

In this course, you will learn all strategies, basic options pricing, and option market mechanics.  These range from spreads to single option positions. 

Some strategies work best in stocks — others in futures.

You will be able to recognize when and in which markets each strategy is most effective. There are several strategies you will come to recognize as bad in any market or market condition. 

Some of these bad strategies may surprise you. 

Learning will be achieved through the following sections. 

  • Section 1: Welcome to Option Trading!
  • Section 2: What the Kardashians Can't Teach You About Options!
  • Section 3:  Option Pricing De-Mystified!

Learn From a Master

I am Dr. Scott Brown.  I am a seasoned option investor with numerous large double or triple digit returns under my belt.

I don’t know anybody willing to teach you the way I trade.

They are better off tending to their investment knitting than answering your questions.  I however, am trained to train them and thus you. 

I hold a coveted Ph.D. in finance from the University of South Carolina.  It cost the Darla Moore School of business a half a million in faculty costs to train me … to train you. 

My financial expertise is unique in that I also hold a master of international financial management from the #1 ranked MBA program Thunderbird, per the U.S. News and World Report. 

What’s in This for You? Discover How I Garnered 357.1% in 111 Days!

You must be asking yourself what you stand to gain from this course. What you are about to learn will allow you to attempt to set up real trades like this,   

Last fall I acquired in the money calls on Fiat Chrysler Automotive N.V. (ADR: FCAU) at a price of $1.0933 and $0.9000 for 419 contracts controlling 100 shares each for a total premium cost of $44,491.95 on November 8 and 10 of 2016.  On February 24 and March 1 of 2017 I sold the position for $160,908.69.  This dished up a total cash profit of $116,416.74 in 111 days for a return of 261.66%. 

The first scale of the campaign cost $4,832.16, sold for $22,087.71 profiting $17,255.55 for a return of 357.10%.   Honestly, if 10 years ago you would’ve told me that triple baggers like this are possible I would have scoffed!

I cannot promise you these returns. But I can show you how I got them.

The Buzz About This Controlled Leverage Option Investment Training

March 7, 2016, Jan Larson, I  hate to miss class.  They are always so clear and informative.  Like nothing else I've ever listened to. Jan


Dear Doc Brown, I am writing this email to express my heartfelt gratitude for this course you have put up.

I have completed the course and the reading part, and it has brought lot of light and richness to my perception of viewing markets. I shall come back to you to share with you how well did I fare. That would be another story, another time. As off now, only wanted to tell you that just viewing your lectures, reading the book has brought me lot of joy in itself. Thank you very much... May the creator bless you with abundance of love, laughter and happiness ! Sincerely, Rajkumar Mehta


I am doing great for a 67 year old man! My investments are doing OK not as good as your. I really like your 3 stock portfolio . I have too many stocks in my portfolio too many small positions. You have made me a believer, just having a hard time converting over to just 3 stocks! Maybe in the near future. You are doing a great job teaching us and I really appreciate all your knowledge and you sharing it with us!!! Thanks, Leonard Saunders


Join this program now if you are serious about mastering options!

Your most precious recourse is time.  Every day that ticks by without this knowledge is a dreadful delay in your financial mastery. 

The contents of this course are guaranteed to be true to the academic literature. Join now while you still have access to me, a Ph.D. holding research professor in finance. -Doc Brown

P.S. Less than half of households are invested in the stock market. Yet stocks offer the highest returns. What’s holding you back?

P.P.S. As Victorian British novelist Mary Anne Evans sagely expressed as George Eliot “It is never too late to be what you might have been.” Enroll now.

Who this course is for:
  • Students interested in options should dive right in. Compulsive gamblers not welcome.
Course content
Expand all 12 lectures 01:21:28
+ Welcome to Option Trading!
3 lectures 11:07

I am Dr. Scott Brown. I hold a Ph.D. in finance from the University of South Carolina. I am a professor of finance of the AACSB accredited Graduate School of Business of the University of Puerto Rico

Just 5% of all business schools in the world enjoy AACSB accreditation.

MBA degrees from these schools are highly prized.

I am teaching this course to help you avoid disaster.  Many investors wipe out in option markets due to over-confidence.

How a $20K Investment Turns into $1.2 M in 10 Years

Here are a couple of unbreakable rules

Make sure all these items are present…

First, let me clarify something: Many people lose money trading stock options.

The business is as tough as crab fishing the Alaskan waters. But returns can be eye-popping if you develop an edge. Cornwall Capital, has extracted 51% annually from the stock market over the last decade blossoming every $20k invested into $1.2 million.

Below are the rules academic research has shown is the best way to trading options:

Rule #1

Buy in-the-money calls on a couple of the strongest stocks you can identify trading across the NYSE, AMEX, and NASDAQ. Go out at least 6 months. 

Rule #2

Utilize the anomalies of momentum, price impact, and post earnings announcement drift (PEAD) to add a few percentage points onto the 9 to 10% geometric expected return of the averages. 

Rule #3

Focus on identifying the elephant in the room.  These are obvious-after-the-fact business franchises that make headlines and rapidly become one or two-word household names. 

  • Amazon.
  • Google.
  • Apple.
  • Facebook.
  • Fiat-Chrysler.
  • Netflix

These new, fast rising firms attract the most capital in the market.  These behemoths are partially owned by activist investors who batter executives into doing the right thing for you. 

Rule #4

Focus most on controlling your downside and the rest will follow.  Limit order strops only partially help.  You must be on your computer screen throughout the day to trade calls. 

Rule #5

Focus on options where (1) implied volatility is low (2) the share price is rising and (3) the indexes are bullish. This is when you will initiate your best trades. 

This course is for anybody interested in options. 

In this course, you will learn all strategies, basic options pricing, and option market mechanics.  These range from spreads to single option positions. 

Some strategies work best in stocks others in futures.

You will be able to recognize when and in which markets each strategy is most effective. There are several strategies you will come to recognize as bad in any market or market condition. 

Some of these bad strategies may surprise you. 

Learning will be achieved through the following sections. 

  • Section 1: Welcome to Option Trading!
  • Section 2: What the Kardashians Can't Teach You About Options!
  • Section 3:  Option Pricing De-Mystified!

If you have any questions post them on the message board for all students to learn.  Send me a personal message otherwise.  Welcome to controlled leveraged investing secrets only I am willing to share with you. -Doc Brown

Preview 03:42

Anatomy of a Stock Option Campaign

Anatomy of a Stock Option Campaign

DOWNLOAD: Course Notes Here.  See resources for this lecture. 

DOWNLOAD: Course Notes Here
+ What the Kardashians Can't Tell You About Option Mechanics!
6 lectures 49:11

This course covers general features of options on individual common stocks. You will discover the tremendous flexibility options afford investors in designing investment strategies.

Option Basics

A stock option is one type of derivative security. This asset is named as such because the value of the option is “derived” from the value of the underlying common stock. Other common derivative securities include futures, futures options, and forward contracts also known as Forex. 
There are two basic types of stock options. 

  • Call options confer the right to buy the underlying asset.
  • Put options convert the right to sell an underlying asset.

The option owner is not obligated to buy or sell anything.  This is not true for the option writer. 
Option contracts that are listed across major exchanges are standardized. This eases trading and price reporting.
Standardized call and put contracts confer rights to 100 shares of stock.

Option contracts constitute legal agreements between the buyer, and the seller of the option. The contract is designed to reduced counterparty risk of either buyer or seller reneging on the deal.

At a bare minimum stock option contracts identify the:
  • identity of the underlying stock.
  • strike price, or exercise price of the option.
  • option contract size.
  • option expiration date, or option maturity.
  • option exercise style (American or European).
  • delivery, or settlement procedure of the underlying from buyer to seller.

Stock options trade across organized option exchanges.  The CBOE is an example, as well as the over-the-counter (OTC) option markets.

The Wall Street Journal has a list of the most active stock option contracts.  This is useful to see which stocks investors are using to trade options.  The first three columns report the name of the option’s underlying stock, the expiration months is next, and then you find the strike price.  A “p” designates a put option and a “c” indicates a call.  The volume is reported along with the exchange in the next two columns.  Open interest is reported. Pricing is per share.  The total price paid is for 100 shares. This is the standard contract size. “Last” is the prior day close price. “Net Chg” is the change in price from the prior day to the close of the quoted session.  “Close” is the final session price.  

The lower two columns and lower top of the third column reports data by individual stock option.  “Option/ Strike” displays company name and the striking price.  The next column is the expiration month which is the Saturday after the 3rd Friday. The final four columns report put and call volume as well as last price of the session.  
The underlying stock, strike, and expiration never change. Call and put price, volume, and open interest do.  
The bottom of the third panel displays aggregate call and put volume as well as open interest by major exchange.  The CBOE is most liquid.

Option Chains

As an option trader, you will frequently refer to an option chain.  This is a list of option contracts and available prices for a security. 

This is referred to as an option chain.

Option chains are available online at the CBOE website ( as well as Yahoo! (

Stock option ticker symbols include letters to identify the underlying stock.

A letter is used to identify the expiration month as well as whether the option is a call or a put.  Twelve letters A through L designate the month for calls; M through X for puts).

Notice these march calls from show the month of March as third letter “C” for the calls and third letter “O” for the puts as reference to the third month of the year.
Not all quotations use a letter to designate the expiration month.  This quote of Facebook (FB) deep in the money calls shows the June sixteenth expiration date as 0616 after the expiration year 17. Finally, the strike is embedded in the code. 
Why Bother with Options?

Are you thinking: “Why buy stock options instead of shares in the underlying stock?” The easiest way to answer this questions is to compare two investment strategies:

  1. Purchase underlying stock
  2. Purchase options on the underlying stock

An Example of Buying the Underlying Stock versus Buying a Call Option

Suppose IBM sells for $90 a share. Notice that this stock certificate of IBM from 1957 is for 100 shares. No small wonder that stock options contracts are based on a standard lot of 100 shares. 
Suppose call options with a strike price of $90 trade at $5 per share at 100 shares per contract. If you invest in 100 shares the cost is:

  • IBM Shares: ($9,000)
  • One listed call option contract: ($500)

The cost to control the same number of shares is eighteen times more expensive at $8,500 with shares of stock than buying the call for just $500.  

But this doesn’t give us any idea how we could win or lose. 

Say the option expires in three months. Finally, imagine that in three months, the price of IBM shares is either $100, $90, or $80.

Furthermore, we can compare the dollar and percentage return given each of the prices for IBM stock. Case I shows that if the stock price rises by $10 that the investor will reap 11.11% on their $9,000 investment of 100 shares at a purchase price of $90 per share.  The same scenario will return $500 on a $500 investment in options.  This represents a 100% return. 

In case II the price remains unchanged.  The $9,000 invested in shares remains intact.  But the options expire worthless.  The loss is the full 100% of the $500 invested in purchasing option premium.  

Case III shows that the stock investor suffers a -11.11% loss if the stock dips $10.  At a final closing price of $80 the option also expires worthless. The loss is 100% but shows that it is capped at the amount paid for premium. 

Preview 06:38

Whether you prefer one strategy over another is a matter for you to decide.

Sometimes investing in the underlying stock is better.  In other cases, investing in the option is better.
You must master each strategy to know which and when apply.

Call options offer an alternative formulation of investment strategies.

You have just seen that the dollar loss potential is lower with call options. This only holds when the investor restricts purchases to the same number of shares.

I showed you that for 100 shares, the dollar potential gain with call options is lower.
But percentage gain with call options is higher. But the negative percentage return with call options is much lower.
This also implies that plopping the full $9,000 into the option rather than shares is dramatically riskier. 

Option Writing

A salesperson must write a contract to transact with a buyer.  For this reason, the act of selling a call or put is termed option writing just as in commerce.

The seller of the option contract is the writer. 

The writer of the call option contract is obligated to sell the underlying stock to the call option buyer. The call option holder (buyer) has the right to exercise the call option (i.e., buy the underlying stock at the strike price).

The writer of a put option contract is obligated to buy the underlying asset from the put option buyer. The put option buyer (holder) has the right to exercise the put option (i.e., sell the underlying stock at the strike price).
Option writing obligates the option writer to buy or sell. The buyer of a call or put has no such obligation. 

To compensate for risk of loss the option writer (seller) receives the price (premium) of the option today from the option buyer.

Exercise Procedure

Option holders (buyers) have the right to exercise their option. The option buyer does not have the obligation to transact. 

But the writer who sells them the call or put does.

The option exercises in a European-style if the call or put buyer’s right to transact is only available at the expiration date. The call or put is said to have an American-Style exercise procedure if this right is available at any time up to and including the option expiration date.

Exercise style has nothing to do with where the option trades. European-style and American-Style options trade in the U.S.  They also trade on other option exchanges throughout the world.

Very Important:  Option buyers may sell their option at any time.  That is, they do not have to exercise.

For that reason, the option seller never knows when the option may be exercised.  If the option is exercised the writer is forced to buy back the put or call.  

This is done regardless of the loss to the seller. 

Payoff vs Profit

The best way to master option investment strategies is to graph initial and terminal cash flows. The initial cash flow is the option price.

The initial cash flow is also called the option premium

The terminal cash flow of an option is the value at expiration. This is realized by the option buyer through exercising the option. The terminal cash flow is the option payoff.

Option Profits are calculated by subtracting the initial option price (premium) from the terminal cash flow option value (payoff). The option premium collected is added to the initial cash flow in the case of selling a call or put... 

Payoff Diagram

This diagram compares the payoff of buying and writing (selling) a call.  The style is European for ease of understanding.

Option payoffs are on the vertical axis.  Possible stock prices at expiration date are on the horizontal axis.  
Notice that the lower limit on the stock price is zero.  But there is no upper limit.  

This is an example of a call option with a strike of $50. 

The long (purchased) call payoffs are zero if the stock expires with the stock price below the strike.  The purchaser of a long call does not have to exercise. 

No rational investor will exercise a call at a loss.  Call options that trade below the strike are out-the-money and expire worthless. 

In-the-money calls are always exercised to either recoup premium or for profit. In this example, the option is in-the-money at equity prices above $50.  The call option payoff is the stock price minus the strike price.  
The long call payoff diagram looks like a hockey stick. Notice that the payoff calculation does not include the premium initially paid for the option. 

What is the payoff if the stock price is $60 at expiration?  Sixty less the strike of fifty is ten dollars. 
The option buyer can sell for $60 after buying the stock at $50.    The writer will lose $10 in this example.  
The buyer of a call option earns $1 for every $1 increase in the stock.  The writer (seller) loses $1 for every $1 gain in the underlying stock price.  

The 4 Core Strategies

Let’s analyze a put with a strike of $50. Payoffs are zero for the put above $50 because the option buyer simply won’t exercise into a loss. Below $50 the payoff to the put option is the strike less the underlying stock price. 
If the stock price drops to $40 the owner of the option profits $10. This is the $50 strike minus the $40 underlying price.

These two payoff diagrams show that profits are unlimited for buyers of calls because there is no limit to how high the share price can rise. The profit to a put buyer is limited to the stock price.   

Alternatively, there is no limit to how much you can lose when selling a call.  The loss to a put seller is limited to the strike but the potential loss could be catastrophic nonetheless. 

This also shows that there are only 4 core strategies in options;
  1. Buying a call.
  2. Selling a call.
  3. Buying a put. 
  4. Selling a put.

When you buy a call or a put you spend money.  When you write a call or a put you are paid money. 

A profit diagram considers the initial amount of cash paid or received. Option premium is subtracted from the graph for a long call or put.  Premium is added in the case of the short written call or put. 

In the case of selling a call the writer makes very little money.  Worse, the seller faces unlimited loss.  

I have encountered numerous accounts of investors made wealthy buying calls — and occasionally in long puts. I have never in my entire career met anybody who is wealthy from selling calls or puts.

The profit diagram shows you why. 

An investor buying calls is set up for the possibility of a massive windfall in fortune.  The put buyer has limited profit but can hedge market weakness in indexes or a stock.  

Option writers, regardless of a call or put have very little potential gain.  If you are trying to get rich in options buying calls offers the greatest potential.  

Writing options is a sucker bet that gives miserly returns at best that are lower than the yield on a short duration rating diversified corporate bond portfolio.   

Let me ask you this? 

If call and put writers make less money than bond investors, why do it?  There is a large movement among investment newsletters pushing investors to sell puts.  

Puts writers have more problems than low or negative expected returns.  The exchange or brokerage forces you to hold a lot of cash in the account through harsh margin requirements.  There are no such costly requirements for buying calls or puts. 

Imaging that you sell a put that is trading for $5 on a stock trading at $100 per share with a strike at $95.  That means that you will receive $500 into your account.

Your brokerage will freeze a big chunk of your account based on the greater amount from one of these two formulas.  

[25% of the underlying price + option ask] – [Out-of-the-Money Amount x 100 x Contract Quantity]

This is 0.25 X $10,000 + $500 - $5 X 100 X 1 = $25 per share.  This is $2,500 capital locked per contract. 

Or they will retain:

Option Ask + [10% of Stock Price x 100 x Contract Quantity]

This is $500 + $10 x 100 x 1 = $1,500. 

The put writer brings in $500 but loses access to $2,500 of capital.  This is a bad deal when compared to buying $500 of calls with no subsequent restrictions in capital. 

Selling puts on stocks under $5 is done on a cash basis. Say you sell to open 10 contracts of puts for $1 on a stock.  You must operate on a cash-secured basis, a broker like Schwab forces you to have $5,000 in your account. 

This is because 10 contracts x 100 shares in an option contract x $5 share price = $5,000). 

This is done to protect the brokerage. If you are put the five dollars stock the cash in your account immunizes the transaction from the possibility that you will not or cannot pay.

In this case the put writer brings in $500 and not only cannot use the money but also loses access to $5,000 of the account from margin. 

Furthermore, the put selling strategy remains profitable only when a stock is bullish.  So, the investor who sells the option brings in a little bit of cash, has a large portion of the account frozen, and faces large losses.  
That is bad from any angle!

The investor who purchased a call or a put pays out a little bit of cash and obtains the opportunity to make a very large return.  That is a far more attractive deal.

Think carefully before selling calls or puts in equities.  Better yet don’t do either.

I get more 1 star reviews on my options courses from equity put sellers than any other source.  Some get very angry at me for “bashing put” selling.  It is hard to bash a bad strategy.  

That is because a bad strategy is … well… bad.  

Put and call selling are the two worst strategies for stock investors.   A recent study entitled “Options as Lotteries” in the Journal of Finance confirms this. Regardless there is always some new sucker out there willing to hop aboard the rising stock put seller’s train. 

Why Options?

Now that you understand the 4 core option strategies here is a tour of compound strategies. These involve multiple options that can be both long and short as well as calls and puts. 

Protective put - Buy a put option on a stock you already own. This is a hedge that protects against a decline in value.  Hedging is a form of insurance.  You will always find that a limit stop order is a way to protect value.  But it won’t guarantee exit. When you need the put to protect you will invariably find it to be too costly compared to a stop on the underlying. 

Covered Call – Here you sell a call option on stock you already own. This exchanges “upside” potential for income. I have never met anybody who became wealthy or could live off a covered call strategy. But you can tunnel income out of a large stock portfolio using this strategy without triggering capital gains.

Straddle – You can also buy a long straddle or sell a call and a put as a short straddle with the same exercise price.

Spreads — When you vary the strike and expiration month with bought and sold options you create a spread. 

Which strategy is right for you?

There are only a few profit scenarios for option strategies. 

  1. Hedging against loss.
  2. Low yield strategies.
  3. High yield strategies.

Hedging strategies come in the form of protective puts in stocks.  Calls can also be protective in futures markets. 

Richard Dennis is famous for using hedging strategies when the markets went severely and unexpectedly against him. 

Low yield income strategies are inferior to a rating diversified corporate bond portfolio with the right duration.  The reason that naked equity put selling and covered call strategies are so popular is that they offer gambling.

You will notice that your portfolio goes nowhere when selling equity options. 

Futures options are different scenarios beyond the scope of this course.  Other possibilities exist in futures options because of high premium prices that increase the attractiveness of selling. 

However, nobody sells a naked put or a call in the futures market and gets out alive.

The best high yield strategy is to buy in-the-money equity calls when a stock is rising.  To make this strategy work you must be good at (1) knowing the trend of equity indexes (2) knowing the true trend of the stock (3) keeping the option delta high and (4) rolling every 6 months or so. 

You can also buy in-the-money puts on falling stock but realize that the expected profit is lower as per our discussion of payout diagrams. 

Stock Versus Futures Options?

There are many option trading strategies available to option traders.  But few understand the key differences between stock and futures options. 

This is important because some of the strategies I will discuss throughout this course work well on stocks or futures contracts.  Others work well only on futures. 

There are a few core differences between futures options and stock options.

The most important is that you can place limit stop orders on stock options.  But stops are not available on options. 

However, it is easier to hedge a futures option position with an offsetting futures contract. 

Finally, futures options trade for a lot more money.  Premium is much higher in futures options.

This means that strategies suffering from poor or negative returns in stock options can be profitable in futures options.  

The Strange Academic Unreality of Arbitrage

Arbitrage exists when you can profit selling something lower than you buy with no risk of loss. The reality is that arbitrage is an unwise strategy to follow.

There are so many participants in the market that any “free-lunch” profits are immediately sucked out.  This happens naturally in the auction pricing process. 

It is highly unlikely that there are trading firms or individuals making large amounts of money on arbitrage due to barriers. These have been covered extensively in the literature. 

This is important because the lack of existence of arbitrage opportunities establishes a fair price for the underlying stock (or futures contract).  This basically says that the auction for share prices is fair.

The Upper Bound for a Call Price

The price of a call option must be lower than the underlying stock price.  Otherwise, a trader could buy the stock and sell the call for a risk-free profit.  Arbitrage would be possible.  Nobody would trust the market and it would collapse if people could arbitrage an unfair risk-free advantage.

What would happen if the call price rose above the underlying share price?

Imagine you found a call option selling for $65 where the underlying stock is selling for $60.

You can arbitrage selling the call, and simultaneously buying the stock.

The worst-case scenario is that the option is exercised and you pocket $5.

The best-case scenario is that the stock sells for less than $65 at option expiration, and you’d keep the $65 in its entirety.

With zero cash outlay, today, no possibility of loss, and a potential for gain the fastest traders would quickly control too much wealth. The investors who move slowly or did not see this would stop trading in indignation and the market for the stock would quickly collapse if the pricing error persisted.

The other possibility is that call selling will reduce the price.  Buying pressure on the underlying stock will increase the share price until there is no arbitrage opportunity. Both the call and the underlying shares are forced into alignment by arbitrage buying and selling in the call and the underlying shares.

Put Price Upper Boundary

If you think it through the put option price must be less than the strike price. Otherwise, unfair arbitrage will be possible and the market would collapse.

What would happen if this were to occur? Imagine a put option with a $50 strike that sells for $60.

Arbitragers would immediately sell the put for cash and invest $60 in the bank.  There would be no cash in the deal and it would be costless. The only risk would be if the stock price drops to zero.

What happens to the guy who writes the put? You would buy the stock for $50. And you would sell the put for $60 and change in interest. 

You would make a riskless $10 if the stock was worth at least $50 when the put expires. 

All the buying in the stock and selling in the option will force the stock price up and the put price down to equality in a reasonably efficient market.

Option Price Lower Boundary

The floor price for any option is zero. That is because an option is disposable. The buyer has no obligation to do anything.

He or she may simply choose to “do nothing.”

Intrinsic value allows us to see a meaningful lower bound. The intrinsic value is the payoff to an option holder if the underlying stock price is static.

Intrinsic Value of an Option

Let S be the current stock price. K is the option strike.  For a call:

Intrinsic value = max [0, S – K ]

The intrinsic value of a call option is either zero or the stock price minus the strike price; whichever is greater.

For a put:

Intrinsic value = max [0, K – S ]

The intrinsic value of a put is either zero or the strike price minus the stock price; whichever is greater.


In the Money” options generate cash when exercised. These have a positive intrinsic value.

The strike price is less than the stock price for calls. The strike price is greater than the stock price for puts.

Out of the Money” options are worthless; have a zero-intrinsic value.

The strike price is greater than the stock price for (worthless) out-of-the-money calls. The strike price is less than the stock price of (worthless) out-of-the-money puts.

when the stock price and the strike price are about equal an option is “At the Money.”

Call Intrinsic Value & Arbitrage

American-style exercise call options must sell for at least intrinsic value; or arbitrage will push values back into alignment.

Imagine that S = $60; C = $5; K = $50. 

Do you see the instant arbitrage?

You could simply buy the call for $5. Then you could immediately exercise the call.

That would buy the stock for $50. Immediately after you would sell the stock at $60.

You would profit with no investment.

Put Intrinsic Value and Arbitrage

American-style exercise put options must sell for at least intrinsic value. Or arbitrage will push prices back into alignment.

Imagine: S = $40; P = $5; K = $50. 

Do you see it?

You buy the put for $5.

Then you buy the stock for $40.

Now you immediately exercise the put. This sells the stock for $50.

You profited $5 with no investment (risk of loss).

Option Price Lower Bounds

Option prices can’t fall below intrinsic value. Or, arbitrage would drive prices back.

In this formula S is the stock price, K is the strike:

                                Call option price = max [0, S – K ]

                                 Put option price = max [0, K – S ]

Four Popular Option Strategies

Employee Stock Options

An employee stock option (ESO) is a call option given to employees by a firm.

These are call options.  Employees can exercise an ESO to buy shares of stock in the company.

There exists a widespread practice of giving stock options to employees. You most likely will, or already own ESOs.

ESO Features

ESOs are not exactly like ordinary call options.

Company details vary. ESOs run for 10 years. ESOs can’t be sold.

The ESO “vesting” period is 3 years. Employees can’t exercise ESOs while working in the company during the vesting period.

The employee loses the ESO If leaving the company before the ESOs are “vested".  The ESOs can be exercised up to expiration if an employee remains employed for the vesting period.

Why ESOs?

Stockholders need to get employees focused on increasing firm profitability — and nothing else. ESOs are a strong motivator because payoffs to options can be large.

If the stock soars both the employee and the stockholder grow wealthy together with no upfront costs to the company.

ESOs can substitute ordinary wages when recruiting employees. 

Repricing of ESO

ESOs are issued “at the money.” One plan I recently reviewed takes the closing price of the stock on December 20 each year as the strike for its new options.

There is no initial intrinsic value to the employee.  The idea is that they must earn it by pushing the share price up.  The employee stock option has value because it is a bet on the future value of the stock that could cough up huge payouts.

The ESO is said to be “underwater” If the stock price falls after granting. Companies occasionally restrike ESOs that are “underwater.”

Stockholders do not like this. Re-striking is a sign that stockholders have lost control of the board of directors.

Controversy Over ESO Repricing

Management claims that underwater employee stock options do not incentivize employees to work as hard as possible driving away employees who leave for companies with better options.

Stockholders are enraged over the practice.  It is a reward for failure.  Poor employee decisions helped a stock fall if the share price is weak in its industry. 

Mediocrity should not be rewarded.

Otherwise, employees are simply profiting unduly from aggregate bull and bear markets.  They are getting free money for nothing. 

Today’s ESOs

ESO are awarded on a regular basis either quarterly or annually.  Employees with long tenure will have a mix of moneyness in their ESO portfolio with some portion that is unvested.

The idea is that the unvested options keep them in the company.

Put-Call Parity

Put-Call Parity is the most fundamental concept in option pricing. It was developed by Vanderbilt University finance professor Hans Stoll. 

Put-Call Parity is most easily grasped analyzing option prices with European-style exercise. European options trade off the exchange. 

They are common in the interbank foreign exchange (Fx) market.  Bankers use these to create custom contracts between two large banks, currency traders or combination thereof.  

Professor Hans Stoll told me one day that he noticed in the data that the difference between the call price and the put price equals the difference between the stock price and the discounted strike price. His paper in the Journal of Finance set forth the rules for the Put-Call Parity pricing relationship.

The Put-Call Parity Formula

e-rT is the discount factor. Ke-rT is thus the discounted strike price.

The symbols in the formula are:

  • C is the current call option price
  • S is the current stock price
  • r is the risk-free rate of interest
  • P is the current put option price
  • K is the strike price of option, call or put
  • T is the time remaining until expiration of the option, call or put

The formula can be rearranged to estimate the theoretical strike:

Why Does Put-Call Parity Work So Well?

Two equivalent assets must sell for identical current prices.  Suppose an investor buys shares in Facebook stock.  Then he or she writes a call and buys a put with identical expiration.  The value of this portfolio at the expiration is shown in the table.

This shows the payoffs for these three assets at expiration. If the stock is above the strike St > K. In this case the put expires worthless.  The investor who sells the call has to pay the buyer -(St -K).

If the share price ends below the strike St<K. The call option is worthless and the put profits K-St.

Regardless of the movement of the underlying share price the value of this 3 asset portfolio is always equal to the strike.  The return to this portfolio is riskless and should be priced the same as other riskless assets such as a 3-month Treasury Bill paying Ke-rT.  This portfolio is formed by first buying the stock and a put then selling a call which we have determined must equal the discounted strike price:

S + P – C = Ke-rT.

Put-Call Parity with Dividends

Stock prices drop after dividend payments — this is a disgorgement of cash.  A factor must be added for the reduction in firm value by the dividend payment.

C - P = Se-yT - Ke-rT

Under all scenarios the portfolio is worth $K at expiration.  It is hedged, it is riskless.

The current value of this portfolio is $Ke-rT or arbitrage will occur. The current price buying 100 shares and a put net writing a call, should equal the cost of a risk-less security worth $K, maturing on date T.

This also means that when the strike and share price are equal that the call price must be greater than the put price: S = K (rT > 0) -> C > P.

Employee Stock Options (ESOs)

Index Options

An option on a stock market index is a stock index option. The most popular are options on the S&P 100, S&P 500, and Dow Jones Industrial Average (DJIA).

stock index options have a cash settlement procedure — the actual delivery of all stocks on the index is not feasible.

When an option expires in the money, the option seller pays the option buyer the intrinsic value for calls or puts.

Index Option Trading

Here you can see the major options on indexes.  The SPX is the most commonly traded.  OEX options used to be the leader.  But now SPX options are used more frequently by money managers. 

Notice that the SPX and OEX options are specifically quoted by strike due to the importance of these two option chains. 

The Options Clearing Corporation

The private agency that guarantees the terms of an option contract if exercised is the Options Clearing Corporation (OCC). The OCC originates all contracts and clears option trading on U.S. exchanges.

The OCC as well as the exchanges are regulated by the Securities and Exchange Commission (SEC).

The OCC page is

The Two Best Stock Options Strategies in the World

Here is a review of each of the major strategies options traders and market makers employ.  But first here are the two best.

Long Call

This bullish strategy is accomplished in just one transaction.  Many option books and courses will write something foolish such as this is a “beginner” strategy. Don’t be fooled.  This is your meat and potatoes strategy.  The truth is that studies show that the long call offers the highest expected return of any option strategy.  A big advantage of equity calls is that limit orders stops may be placed on the long premium.  Stops on futures call options are available but the market can gap over the limit in a flash crash. 

Long Put

This bearish strategy is created by purchasing a put.  This strategy offers the second highest expected returns of all option strategies. 

These are the two strategies that offer you the best expected returns in the stock market. 

The Following Strategies are the Four Horseman of Financial Apocalypse

The following strategies do not make money in any market and should be avoided at all cost.

Short Call

Nobody sells calls naked.  It would be insane considering the lognormal distribution of stock returns.  This distribution is one in which the market is not only more likely to rise than fall but rises more and faster than anyone expects.  Selling naked calls would be like stepping in front of a train. 

Don’t do it.

Covered Call

People normally own the stock on which they sell the call.  This position is the covered call.  The problem with this strategy is that the potential profit on the call is limited to the premium brought in when sold. And the fact that the call is short also limits the profit on the underlying stock. 

I tried this strategy in the 1990s.  I quickly learned that owning the stock outright is far more profitable than selling the covered call. 

Avoid this strategy and variant, the Covered Call Collar - This is identical to the covered call except that you use the money from selling calls on stock you own to buy the same number of puts. 

Short Put

I have already explained how selling puts locks up a lot of capital with massive potential losses for a tiny bit of premium at the sale.  I have already explained why I not only do not sell naked puts.  I also have never heard of anybody getting rich selling puts or calls. 

This strategy is toxic to your financial health.

Notice that if you combine the short put and short call that you get a short straddle or short strangle as explained below.  These are also toxic because the small amount of premium will never make up for the losses of sudden move. 

Covered Put

I do not short sell stock.  But I do have a colleague who does and seems successful. 

The covered put is for people who short sell stock.  Furthermore, the trader believes that the stock is long term bearish but short or medium term neutral. 

This position is created by selling at the money puts with enough time to expiration to cover the consolidation period.

This is another losing strategy.  Avoid it.  

Index Options

Futures Option Strategies that Might Make Sense

Now I will discuss a myriad of other option strategies. Don’t take any of these at face value. 

Study and analyze each before you adopt.  Test and decided for yourself if any of these can make you money. 

Always remember that stock options are very cheap as compared to expensive futures options.   Since long calls and puts on stocks are cheap it doesn’t make any sense to sell stock options. That means that each of the strategies below are best tested in futures markets.  

However, a friend of mine who traded extensively for Enron is convinced that every single strategy below was designed by clever brokers to suck money out of your account.  This is especially troubling considering that my friend is a broker. 

So, approach each of the strategies below testing for flaws rather than riches. 

Long In-The-Money Strangle

This is also called a long gut.  The position is set up buying an in the money call and put with roughly the same moneyness.  This will always be far more expensive than simply buying an in-the-money call or put. 

You should not take positions when you are uncertain of market direction. 

That said this is an interesting strategy to test in a market that is in a long narrow consolidation.  I don’t use them because better performance comes from a directional bet on a call or put after or as the market breaks up or down. 

Then I use a stop on my stock options because this is cheaper than a strangle (gut). 

Strap Strangle

Buy more calls than puts testing from an initial 2:1 ratio.  Adjust with learning. 

Strip Strangle

Buy more puts than calls at an initial two to one ratio.  Then adjust. 

Long Straddle

A long straddle is the same as a strangle except that the strike of both the puts and calls are at the money. Again, you should not be trading if you do not have an inclination of the major trend.  And you can place limit order stops on equity options.  I have found this strategy to be needlessly costly.  I tried it at the beginning when I was learning options in the 90s.  But I no longer find any use for it.

Strap Straddle

This is a derivative of the long straddle that can generate greater profits.  Buy fewer puts than calls. Test this strategy starting with a 2 to 1 ratio of calls to puts. 

Strip Straddle

This is another modification of the long straddle.  Buy more puts than calls. Start with a 2 to 1 ratio then adjust as you gain experience.

Call Bull Spread

This strategy is employed by buying at the money calls and selling an equal number of out of the money calls.  The idea is to reduce the cost of buying calls. 

The disadvantage is that profits are capped at the strike of the short out of the money calls. 

Call Ladder Bull Spread

Buy at-the-money calls, then write calls at different strikes.  The premium from selling the short calls compensates for the cost of the long calls.  

Set the first short strikes at the level you think the futures price will rise to.  Then sell more calls at the next highest strike. 

Call Bear Spread

If you buy out of the money calls and sell the same number at the money you will have created a call bear spread.  This spread is a lower cost alternative to the long put.  But the profit is even more limited.  The potential profit of the long put is much higher in bearish markets.

Put Bear Spread

Buy at-the-money puts.  Sell puts out-of-the-money at the level you expect the futures to be at upon expiration.     All transactions should be at the same expiration.

Bear Put Ladder Spread

Buy at the money puts. Then sell puts at the level you expect the stock to obtain at expiration.  Then sell more at the next lowest strike.

Put Bull Spread

Write puts at a high strike. Then buy puts at a lower strike.  

You need to write puts based on the underlying security that you are expecting to rise in price (using the sell to open order), and buy the same number of puts based on that security (using the buy to open order). This is a way to reduce the cost of selling puts.

Call Short Calendar Spread

Buy short term and sell far expiration calls at the same strike at the money. You will make the difference between the short and long premium value.  

Put Short Calendar Spread

Buy short term puts and sell those at a later expiration at the same strike.  A variant is the short diagonal calendar put spread where the long puts are purchased out of the money. 

Calendar Straddle

You create a calendar straddle by writing near term calls at the money. Then you write puts at the money at the same expiration as the short calls.

This brings in premium you use to offset the cost of buying at the money calls with a later expiration date. Then you can buy later month puts at the money at the same later date as the long calls.

Calendar Strangle

This is created by using a combination of near term short calls and puts to finance later term long calls and puts as with the calendar straddle.  The only difference between this and the calendar straddle is the use of out of the money strikes. 

Long Call Calendar Spread

Write near term and use the money to reduce the cost of long term calls at the same strike as a horizontal spread.  Strikes are normally at the money or out of the money (cheaper). 

Long Put Calendar Spread

This is the same procedure as the call calendar spread above but uses put options.  This is a market neutral strategy. 

Call Ratio Spread

Write more calls than you buy in a 2:1 or 3:1 ratio.  Buy at the money and write a higher out of the money strike.  

Call Ratio Backspread

Buy two at the money and sell in the money calls with the same expiration. 

Put Ratio Spread

This is the same as the call ratio spread but uses puts.  Buy at the money and write a lower out of the money strike.

Call Ratio Backspread

For every short in the money call buy two at the money at the same expiration. You have to bring in more money from the calls you write than it costs to purchase. Set this up as a credit spread. 

Put Ratio Backspread

Buy twice as many puts as you write at the same expiration as a credit spread. Buy at the money and sell in the money to do this.

Ratio Bull Spread

Buy at the money calls. Write twice as many as you sell at first.  Then vary the ratio and strikes as you learn. The challenge is to estimate the correct ratio of long to short calls as well as the correct choice of strikes.

The decision to set this up as a credit or debit spread is important. 

A debit spread will lose if the price falls or channels. A credit spread will profit in the same scenario.

Ratio Bear Spread

As before you buy and then write a larger number of puts.  As before, it takes knowledge, practice and experience to become skilled at setting the appropriate ratio of long to short calls as well as strike levels. 

Short Ratio Bull Spread

Buy more calls than you write at the same expiration on the same underlying futures contract.  The goal is to reduce the cost of the calls.  To test this strategy, try a 3:1 ratio first. 

It is possible to create an extremely low cost position in futures with this strategy.

Short Ratio Bear Spread

Follow the same steps as above. But use puts rather than calls. 

Buy three calls for every one you sell on the same futures contract.

Condor Spread

This consists of four trades at the same expiration. First buy deep in the money calls.  Then write in the money calls with a higher strike than the long calls.  Buy deep out of the money and write less out of the money puts with a lower strike than the long puts. 

Short Condor Spread

Buy-write deep in the money calls where the long is above the short strike.  Then write far out of the money calls where the long strike is below the short.

Iron Condor Spread

To set this up buy and sell out of the money calls where the short strike is below the long. Then buy and sell out of the money puts where the short is above the long strike.

Reverse Iron Condor

A reverse iron condor is buying and selling out of the money puts with the short strike below the long. Then buy and sell out of the money calls with the short strike is above the long.

Bull Condor Spread

Write calls with a strike at the low end of the price fluctuations you expect by expiration. Than write more at the high end of your futures price forecast range.  Then you buy calls with a low strike and sell calls with a high strike. 

Long Albatross Spread

This is the same as the condor spread but the strikes are wider.

Short Albatross Spread

Short Albatross Spread is the same as the short condor spread but employs a wider difference between the strikes.

Iron Albatross Spread

This is a wide iron condor spread. The iron albatross spread is set up like the iron condor spread, except that long and short options are further out of the money.

Reverse Iron Albatross Spread

This is like the reverse iron condor spread, but with wider strikes.

Butterfly Spread

This is established at the same expiration and equidistant strike.  Buy and sell the same amount of in and out-of-the-money calls. Then write twice as many at-the-money calls.

Butterfly Short Spread

Same as above regarding same expiration and equidistant strike.  Sell in and out-of-the-money calls.

Purchase twice the amount of at-the-money calls.

Bull Butterfly Spread

This is best set up as an inexpensive debit spread.  The strikes are different from the standard butterfly spread. 

Write calls at the expected future price of the stock upon expiration of the option.  Buy one call for every two written at the next lowest strike and then another at the next highest. 

Bear Butterfly Spread

This is another strike modified butterfly spread. Write puts at the expected future price of the stock upon expiration of the option.  Buy one put for every two written at the next lowest strike and then another at the next highest. 

Iron Butterfly Spread

This is a credit spread where you,

  1. Buy calls out-of-the-money
  2. Sell calls at-the-money
  3. Buy puts out-of-the-money
  4. Sell puts at-the-money

Each leg should have the same number of options at the same expiration. The strikes of the out of the money puts and calls should be equidistant from the underlying price.

The farther out of the money the strikes are, the higher the likelihood of making a profit. This is due to a wider range of profit possibilities. But this increases maximum losses to the downside.

Iron Butterfly Reverse Spread

Put on this position with these steps with the same number of options at the same expiration.

  1. Sell out-of-the-money calls. 
  2. Buy at-the-money calls.
  3. Sell out-of-the-money puts. 
  4. Buy at-the-money puts.

The cheaper the position, the greater your risk of loss the closer the written strikes are to the out-of-the-money options. 

Box Spread

The box spread is a complicated strategy that involves four transactions.  WARNING: This strategy is so expensive for the retail trader in commissions that it has been dubbed the alligator spread. 

Synthetic Covered Call

Buy a deep in the money call and sell an out of the money call at the same expiration.  

Futures Option Strategies that Might Make Sense
Quiz 1
5 questions
+ Option Pricing De-Mystified
3 lectures 21:09

Option Valuation Explained

Now I am going to take you by the hand and will guide you through option pricing.  First you will discover the details of the Black-Scholes-Merton option pricing model.

I will show you the market’s forward-looking uncertainty gauge called "implied volatility."

Most importantly I will show you how to set up spreadsheets to easily crunch otherwise hard calculations. 

What is an Option Worth?

This is not an easy question.  But a mathematician named Bachelier worked it out in 1900.

Louis Jean-Baptiste Alphonse Bachelier lived from 1870 to 1946.   He successfully applied the mathematics of Brownian motion to the option pricing problem. 

The Bachelier model is the precursor to all other option models.

To grasp the model first, consider that at expiration, an option is worth its intrinsic value. put-call parity allows for pricing options before expiration. 

But to do this you need to know the put price to calculate the price of a call. And you need to know the call price to calculate the price of a put.

A good option pricing model will tell you the price of a call without the need of knowing the price of a put. 


Professors Fisher Black, Myron Scholes, and Robert Merton worked out the modern model of option pricing.  Fisher Black and Myron Sholes published the first paper on the subject in the Journal of Political Economy in 1973.  See Fischer Black and Myron Scholes. 1973. “The Pricing of Options and Corporate Liabilities.” The Journal of Political Economy, Vol. 81(3) 637-654.

Based on Bachelier’s work the Black-Scholes option pricing model calculates the price of a call option before maturity without knowing the price of a put option. 

This modern formulation is by Professors Fischer Black and Myron Scholes at the University of Chicago.  It made option pricing a lot easier. It is no coincidence that the CBOE was launched shortly after the Black-Scholes model was published.

Finance professionals now use an extended version of the model termed the Black-Scholes-Merton option pricing model.

This incorporates important theoretical contributions by professor Robert Merton at MIT Sloan School of Management.

The Black-Scholes-Merton Option Pricing Model

The Black-Scholes-Merton option pricing model formulates the value of a stock option from six factors:

  1. S, the underlying stock or futures current price
  2. y, the underlying stock dividend yield
  3. K, the option contract strike price
  4. r, the risk-free interest rate
  5. T, the time to option expiration
  6. σ, the underlying stock or futures price volatility

The Black-Scholes-Merton Option Pricing Formula

The price of a call option is a combination of these six factors: C = Se–yTN(d1) – Ke–rTN(d2)

Ditto for the price of a put option: P = Ke–rTN(–d2) – Se–yTN(–d1)

Then calculate d1 and d2.

Formula Details

Three common functions are used to price call and put option prices in the Black-Scholes-Merton formula:

e-rt, or exp(-rt), is the natural exponent of the value of the discount factor (–rt)

ln(S/K) is the natural log of "moneyness", S/K.

N(d1) and N(d2) is the standard normal probability for d1 and d2.  The model utilizes the following relationship: N(-d1) = 1 - N(d1)

Example: Computing Prices for Call and Put Options

Here is an example.

  • S = $50
  • y = 2%
  • K = $45
  • T = 3 months (or 0.25 years)
  • s = 25% (stock volatility)
  • r = 6%

What is the theoretical Black-Scholes-Merton option pricing formula price of a call option and a put option?

Here is How to Answer

Calculate d1 and d2,

Now, compute the standard normal pricing probabilities N(d1) and N(d2).

Table of Standard Normal Probabilities

In the old days, we used to use probability tables like this. Here is how to use it. The d1 value of 0.86038 falls somewhere between N(.95) and N(1). These correspond to 0.8289 and .8413 respectively for the d2 value of 0.86038.

The d2 value is 0.86038. 

This falls between N(.85) of 0.8023 and N(.9) of 0.8159.

A linear interpolation …

This allows us to calculate the price of a call option as


Errors of 5 to 10 percent are possible.

You can also use the =NORMSDIST(x) Function in Excel

=NORMSDIST(0.98538), computes 0.83778.

If we use =NORMSDIST(0.86038), calculates 0.80521.

Don’t forget that N(-d1) = 1 - N(d1).


N(-0.98538) = 1 – N(0.98538) = 1 – 0.83778 = 0.16222. N(-0.86038) = 1 – N(0.86038) = 1 – 0.80521 = 0.19479.

This is all you need to price the call and the put.

Calculating the Call Price and the Put Price:

Call Price  = Se–yTN(d1) – Ke–rTN(d2)      = $50 x e-(0.02)(0.25) x 0.83778 – 45 x e-(0.06)(0.25) x 0.80521      = 50 x 0.99501 x 0.83778 – 45 x 0.98511 x 0.80521      = $5.985.

Put Price  = Ke–rTN(–d2) – Se–yTN(–d1) = $45 x e-(0.06)(0.25) x 0.19479 – 50 x e-(0.02)(0.25) x 0.16222

     = 45 x 0.98511 x 0.19479 – 50 x 0.99501 x 0.16222

     = $0.565.

Verify with Put-Call Parity

Assuming European-style exercise.

Verify with Excel

General Option Valuation

Option Price Inputs

Option prices changes when any of six inputs change as I explained in the last slide.

This table summarizes these effects. A call price increases with increasing stock price while the reverse is true for the put.  The opposite is so for increasing strike prices. 

This is measured by delta. 

However, more time to expiration uniformly increases the price of both the call and the put as described by theta.  Ditto for increasing volatility as graphed by vega. Option traders use rho to measure   increases in risk-free rate that enhance the value of a call but diminishes that of a put.

Rising dividend yield retards call value but increases the price of put. 

Underlying Stock Price

Changes in share price have the most effect on put and call option prices. This graph illustrates how call prices rise as put prices fall when the share price increases.

Mapping Theta

Time decay of extrinsic value for a call is more intense than with a put. The decay of premium value is most intense in the last few months.  Again, this affects extrinsic not intrinsic value.  The intrinsic value is the difference between the strike and underlying or vice versa.  Any amount in excess is extrinsic value. 

Probing Vega

The volatility of the Stock Price has a linear impact on both a put and call.  If the standard deviation of share price returns (sigma %) increases so does the price of a call or a put.

Charting Rho

Any increases in the risk-free interest rate will increase the value of a call or decrease the price of a put.  The effect is linear. 

Two Most Important Factors

Option traders can perform simple sensitivity analysis with input prices to learn the effect on the value of the options in a portfolio.

This shows that two factors have the biggest effect over a time span of a few days:

  1. Stock price fluctuations (Delta)
  2. Stock price volatility fluctuations (Vega)

Calculating Delta

Delta measures the dollar change in option price as the underlying stock price changes value.

                                Delta of a Call Option = e–yTN(d1) > 0

                                Delta of a Put Option      = –e–yTN(–d1) < 0

A change in the stock price impacts the option premium value proportionally by delta.

An Example of Calculating Delta: The "Delta" Forecast

The call will increase or decrease by 83 cents for a 1 dollar surge or drop in the underlying stock price.  The put will fluctuate by 16 cents under the same conditions. 

The call delta value of 0.8336 predicts that if the stock price increases by $1, the call option price will increase by $0.83.

If the stock price is $51, the call option value is $6.837—an actual increase of about $0.85.

How well does Delta predict if the stock price changes by $0.25?

The put delta value of -0.1938 predicts that if the stock price increases by $1, the put option price will decrease by $0.19.

If the stock price is $51, the put option value is $0.422—an actual decrease of about $0.14.

Vega Calculations

Vega measures the change in the value of stock options as stock price volatility fluctuates. Vega is identical in impact on the price of both call and put options.

 n(d) is a standard normal density.  

A stock price volatility change of 100% (i.e., from 25% to 125%), increases option prices by about vega.

Example of Calculating Vega: The "Vega" Forecast

The price of a call or put will increase by $6.06 if volatility doubles.

Vega of 6.063 foretells that if the stock price volatility expands by 100% (i.e., from 25% to 125%), call and put option prices will increase by $6.063. This is why I get particularly excited when I find opportunities in quiet markets where implied volatility is at or near annual lows. 

Traders as a rule of thumb divide vega by 100.  If the stock price volatility rises 1% (25% to 26%), call and put option prices rise by about $0.063 (6 cents).

If you set up the spreadsheet to test what happens if the stock price volatility increases from 25% to 26%, you will see that the

Call option price rises to $6.047, an increase of $0.062.

Put option price increases to $0.627, a rise of $0.062.

You will find implied volatility charts such as those found at far more useful than vega.

Option Price Impacts of Gamma, Theta and Rho

Gamma is the rate of change of delta per a $1 in stock price. 

Gamma is very important for option market makers for hedging purposes.  It is not very important for retail option traders. 

Nonetheless it is important for you to understand to help you think through option pricing.

Theta measures option price sensitivity over the time remaining until option expiration.  The helpfulness of theta is an intuitive awareness that time decay is strongest in the last month of an equity option. 

Rho measures option price interest rate sensitivity.  A 1% interest rate change causes the option price to change by rho.

Implied Volatility

The Black-Scholes-Merton input factors equity option pricing model can also give you the demand for options. This is done through implied stock price volatility estimated from the option price. 

This is called implied standard deviation (ISD) or implied volatility (IVOL). Calculating an implied volatility requires all other input factors as well as either the call or put price

Implied Volatility, Cont.

Sigma denotes implied volatility.  The exact value can be found by trial and error with a computer.

This simple closed form formula produces an accurate implied volatility value if the stock price is not too far from the strike.

Example, Calculating an Implied Volatility

Notice that this spreadsheet will give you the implied (estimated) volatility as compared to actual historical volatility.  It is useful to chart these differences over time.  IVolatility dot com allows you to see this data calculated and graphed over time. 

Option Valuation Inputs

Stock Indexes CBOE Implied Volatilities

The CBOE offers data for 2 implied volatility indexes:

  • S&P 100 Index Option Volatility (VIX)
  • Nasdaq 100 Index Option Volatility (VXN)

These key volatility indexes are calculated using implied volatility measures from eight options:

Four calls with two maturities:

  • slightly out of the money
  • slightly in the money

Four puts with two maturities:

  • slightly out of the money
  • slightly in the money

These indexes give investors market volatility information over coming months.

VIX vs. S&P 100 Index Realized Volatility Versus Implied

Notice that implied volatility can vary a lot between the VIX and historical volatility.

VXN vs. Nasdaq 100 Index Realized Volatility Versus Implied

Notice the same pattern in the VXN. 

Hedging a Large Stock Portfolio with Index Options

Many institutional money managers employ stock index call options to hedge the stock portfolios they manage.

The number of option contracts the manager must buy is calculated with this formula:

This is not a set-and-forget strategy. Regular rebalancing maintains an effective hedge over time.  That’s because over time:

  • Underlying Value Changes
  • Option Delta Changes
  • Portfolio Value Changes
  • Portfolio Beta Changes

Example: Calculating the Number of Option Contracts Needed to Hedge an Equity Portfolio

Imagine that the $45,000,000 portfolio you manage has a beta of 1.10.  The indexes are looking weak.

You decide to hedge the value of this portfolio with the purchase of put options.

The put options have a delta of -0.31

The value of the index is 1050.

The hedge requires you purchase this amount of put options.

Implied Volatility Skews

Volatility skews (or volatility smiles) describe the relationship between implied volatilities and strike prices for options.

Recall that implied volatility is often used to estimate a stock’s price volatility over the period remaining until option expiration.

Graph of Volatility Skews

The Black-Sholes-Merton model assumes that there should be just one value for implied volatility.  This is not true. 

When you graph the implied volatility by strike a variety of skewed patterns emerge including smirks and smiles.  These arise because of differences in demand for different strikes. 

A strike that has higher demand will be more actively traded.  This drives up the price.  This is expressed as variation in implied volatility across all strikes.  iVolatilty dot com is an excellent website that graphs this relationship automatically. 

Option Stops Explained

Risk control is vital in the stock market. 

This is done through stop orders. There are two ways to place stops on stocks or options: market or limit. A market order stop on an option converts into a market order when hit. 

You simply set the stop price.

A limit order stop is more complex but gives you more control over the trade. 

The Limit and the Stop Price. 

Here is an example of placing a stop on a stock or option trading at 5.00.  To place a stop 5 cent gap at 4.10/ 0.05 you would place the following order as sell for stocks or sell to close for options as,

  • Stop: 4.10
  • Limit: 4.05

If the market is moving fast and there is no trade at 4.05 the option price will end up trading below the limit level as the price plummets.  The stop price in this case is the trigger to activate the order. 

Regular Trading Session Only

If the market trades at or back up to 4.05 the order will be filled at the limit.  In this case the sell limit stop order should be set to activate on the ask rather than bid.

There are always fewer option contracts trading than shares of stock.  Hence expect wide bid-ask spreads and lots of slippage.   

Options only trade during the regular trading session from 9:30 A.M. to 4:00 P.M. Eastern.  The underlying stocks trade from 8:00 AM to 7:00 PM with extended hours in the evening and early morning.

If any bad news hits the market or your stock watch out. The market could open far below the closing price of the prior session. 

Beware Flash Crashes

A stop market order will fill at the prevailing price.  This is lethal in a flash crash such as 2015 when the market opened 800 points down upon contagion from China. 

The market quickly rebounded and traders using market orders were hammered. 

In the case of a major market crash in 2007 the investor using limit orders stops would be under water but would not be in position to wait for the market to recover to the limit price of the stop.  He or she would have to cancel and exit on market or adjust the limit sell order to the prevailing price.

A third way to protect options is to use alerts.  These can be set up in the system.

When the market falls through a level you predetermine a message goes to your handheld. Then you can exit on a market or limit order upon your discretion.

A fourth approach is to buy a few shares along with your position.  Sell your options when you get stopped out of the underlying on a limit order stop.  Favor limit order stops and steel yourself to close positions that gap below.     

Class Project

Analyze and select an in the money call trade.  Describe,

  1. The stock.
  2. The option.
  3. The indexes. 

Thank You!

This is the end of this course. Please send me a message with comments about this training.  -Doc Brown

Implied Volatility Indexes
Quiz 2
5 questions