Advanced Stock Options for Serious Equity Investors!

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Master secrets of controlled leverage investing. Use techniques employed by masters like Warren Buffet or George Soros.

1,280 students enrolled

What Will I Learn?

- Discover the vast yet small differences between American puts and calls and their European style kissing cousins.
- Map the span of puts and calls across stocks, futures and forex.
- Fathom how new financial assets are created from other assets.
- Master the concept of option premium so similar to insurance payments.
- Measure the intrinsic value between the strike and underlying price.
- Clarify complex jargon such as the exercise and strike which have the same meaning.
- Learn to use position diagrams for deep economic intuition into option trading strategy.
- Fully visualize the break-even point of any option transaction.
- Use these keen insights to develop the put-call parity relationship.
- Map out the valuation limits on both puts and calls.
- Use the binomial model to solve any option valuation problem.
- Correctly gauge how up and down underlying movements influence option valuation.
- Use option delta as the ratio of the spread of possible premium values over share price possibilities.
- Arrange valuation modeling within a risk-neutral universe.
- Link the sigma volatility of underlying stock to option premium price.
- Employ the binomial option pricing model of finance professors Cox, Ross, and Rubenstein.
- Watch the binomial model converge to the Black-Scholes.
- Calculate values and probabilities at each node of a binomial model.
- Estimate the direct measure of rise in a stock.
- Recall Euler’s number as equal to 2.71828.
- Harness the ultra-precise power of continuous time mathematics to calculate the true value of your options.
- Pull delta values from cumulative normal distribution tables of the Excel function NORMSDIST(d).
- See how increasing the exercise price ramps up put value but hammers calls.
- Map out each of the components and variable of the Black-Scholes pricing model.
- See how far times to expiration are more costly but offer far more protection against adverse underlying share price movements.
- Become wise as to the meaning of the log-normal distribution rightward skew and limited downside.
- Learn to expect more extreme profitable movements than you would otherwise expect.
- Calculate call values for employee stock options gifted to dirt bag CEOs and their crony crew.
- Utilize the VIX to measure aggregate fluctuations in market wide implied volatility.
- Recognize that there are at least five other option pricing variations in addition to the binomial and the Black-Scholes models for unique market situations.
- Recognize your real option to wait.
- Understand real options to expand.
- View trimming down or abandoning as a real option for corporate managers.
- See the ability to adjust or vary production and output as a valuable real option.
- Recognize the value of a real option as the difference between project NPV with and without the option.
- Use real options to re-value negative NPV projects with vast turnaround potential.
- Graph out the real option to wait.
- Diagram the loss in option value if a competitor beats firm managers to the punch.
- See how the ability to wait and do nothing offer higher real option values.
- Memorize the relationship that Real Option Value = Intrinsic Value + Time Premium

Requirements

- Basic high school math.
- This is an advanced option course and a basic understanding is helpful but not required.

Description

**How's this for Stellar Profits?**

- 6.24% one day profit of
**$9,760.05**on FB calls [9-2-2014] - 2.75% one day profit of
**$3,430.87**on FB calls [10-21-2014] - 9.39% one day profit of
**$8,054.73**on FB calls [12-18-2014] - 26.67% one day profit of
**$21,607.50**on AAPL calls [1-28-2015] - 16.49% one day profit of
**$16,390.50**on AAPL calls [1-29-2015] - 6.47% one day profit of
**$7,740.00**on APPL calls [2-10-2015] - 6.25% one day profit of
**$15,688.10**on APPL calls [2-23-2015]

**They add up.**

Had you been one of the lucky few who followed **Dr. Brown** in 2013 and 2014 you would have watched him extract a 60 and 66% return — *not on one lucky trade* — on account. These are the returns in his single stock **option portfolio**. Read on to find out how you may reap these kind of gains this year with this best kept secret from the academic **genius **side of Wall Street.

In this course you will be introduced to the **one perfect option strategy**. The buzz is palpable ...

**[Student email on 1st of October 2015]**"*On another note, I wanted to tell you how well presented I thought the options course you put on udemy is. I've liked all your productions but this one is probably the best, in my opinion. Very nicely articulated in a relaxed but poignant manner, great graphics that engage the viewers attention while absorbing the audio material, and providing a simple, usable and profitable method for option trading. The best part is you cut right through all the other crap that brokers and charlatans use as their mainstay for option services and slap them down with academic studies that disprove it all. Really, really nice job :) Cheers!*"**-Mountain Man**

Dear fellow **investor**,

My name is **Scott**. I am a successful academic **expert **in options with extensive actual experience as a professional trader for my own account. By successful I mean that I am able to make **significant **amounts of money for my family. I watch over our finances as a financial **steward**.

Sometimes I am asked how I was able to become so **successful **in such a difficult game.

I became obsessed with finance from trading **futures**. This led me to obtain a Ph.D. in finance from the **University of South Carolina**.

This was no small **feat**.

The Ph.D. in **finance **at the University of South Carolina accepts just two students every two years from large application pools. The two applicants who win admission have tuition waived for **free**.

**Competition **is fierce because we live on pensions during the 5 years it takes to earn a doctoral degree in financial economics. Nobody with a finance Ph.D. from an **AACSB **business school owes student loans.

The **American Assembly of Collegiate Schools of Business (AACSB) **provides internationally recognized, specialized accreditation for business and accounting programs at the bachelor's, master's, and doctoral level.

**Senator Elizabeth Warren** shows that a university professor with a highly quantitative Ph.D. such as finance almost never endures bankruptcy because of this. It also helps that we **command **high pay.

**But If You Thought Medical School Was Tough ...**

For this reason about a **hundred **new doctorates in finance become new professors each year at the worlds best business schools.

Another **reason **we make more is that we are such hard workers in finance. This is one of the last old world style **apprentice **systems.

We work 365 days per year as research assistance to the brightest financial academics in the world.

The finance faculty from whom we strive to earn a **doctorate **in finance owns us. After years of grinding through tomes of mathematical **derivations **half of us become finance professors with medical school faculty sized **salaries**.

That's because the other half pumps up our market price by starting on **Wall Street **at $350K per year or more.

One of us in my **class **did just that. The last family photo we saw was that of his wife draped over the **Maserati **in front of their mansion in the Hamptons.

When I caught up to him this **summer **he corrected me. It was not the Maserati, they has **sold **that the year before.

She was draped over the new **Lamborghini**.

I chuckle when a **Wolf of Wall Street **misleads individual retail investors into believing that we teach because we can't trade. The reality could not be further from the truth. Go back and peruse my personal **results **I have posted above.

These results have been audited by **TD Ameritrade** and **OptionsXpress**.

**HEADS UP!**

Stop reading investment newsletter **recommendations **written by drunks, con artists and imbeciles. Learn to find your option trades on your **own**.

Sidestep these bad option trading strategies that will bleed your account dry faster than a **one armed bandit** on the Las Vegas strip. **Losing **stock option strategies are routinely touted by marketing cheats, scoundrels and incompetents operating major investment newsletters.

And it's official that I am at the top of the **Wolves of Wall Street enemy list**. My shocking revelations of Wall Street's investment newsletters have boosted me right up to** numero uno**.

Now, **making #1 **on this list is not such an easy feat.

After all, professor **Bill Christie** of Vanderbilt university stirred up quite a list of “enemy" brokers, directors, presidents and the CEO. Dr. Christie's research revealed that the **NASDAQ **was ripping off millions of retail investors with illegally excessive transaction costs in the form of an artificially wide bid ask spread.

So how did I — another simple finance **professor **from a major state university — make it to the top?

Maybe it was my exposé on the investment newsletter industry that was featured in the **Certified Financial Analysis CFA Digest**. This research was published at the top of financial academia in the prestigious academic journal **Financial Management**.

- Brown, Cao and Powers (2013)
*Do Investment Newsletters Move markets.***Financial Management 42(2).**315-338.

This crucial study showed that widely subscribed investment newsletters in the **Mark Hulbert Financial Digest** offer nothing but loss and emotional pain to their subscribers — despite routine claims of return percentages in the hundreds.

**Study This or Go Broke! **

It could be for this reason — or a dozen other **revelations **like them. The kind I **publish **every month in this course's bulletin, “*Strategic Option Intelligence*."

In **fact**, I've been called the “*most fearless financial academic in the world today*."

But you won't read my writing in any **mainstream **financial press. They don't have the — well, let's just say the **guts **— to publish my insights and findings.

In short, I will bring you the **financial stories** that no one else will touch. These are stories that will shape your financial **world **of tomorrow.

I will go **anywhere **and do anything to get the truth. And I will **tell **it to you, no matter who objects.

My **fearless **style has made me a lot of enemies — some of them in the highest places in the Wolves of Wall Street pack.

That is why the **CFA Digest** did a cover piece on my research.

This most **prestigious **paragon of proper financial conduct felt that getting the word out about my research was of paramount importance to you.

**Here Is the Student Response ...**

"*Dr. Scott Brown is one of the sharpest guys I know. Highly recommended.*" — **Alex Green**, New York Times Best Selling author of the “Gone Fishing Portfolio"

“*Most newsletters and trainers want you just trust them that they will make you money. But Dr. Brown is a unique combination of academic prowess and street smarts skill. He is the man to take you from a mere patriot of others to a knowledgeable trader. If you want to add discernment to your tool box and make money in the process, you must learn from the Doctor*." — **Joe Martinson**, Los Angeles, California, USA

"*Keep doing what you're doing. What you are teaching is 100% correct. Marketing is a tough business, especially with the plethora of BS out there on how easy it is to make money trading... Keep it real and grounded in facts and you should attract long term clients who will enhance your service. I really appreciate your efforts in sharing.*" **–F.M.**

"*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 a 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 of now, only wanted to tell you that just viewing your lectures 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**

"*Yep, got it now. Thanks Scott. By the way, the DITM Call strategy seems to be working very well for me...started about two months ago with two positions and both are working well...thanks for that too!*" **— ****Bob Crandalls.**

"*My brain is mush right now (I wish I could say it was from beer). IMy brain is mush because I've just went through ***280** charts in about 30 minutes. WOW! I am as happy as a fat hog in slop. Was this your brainchild? What a great idea. Not only does it really cut through the burden of time and effort, but it seems to instill confidence in me, knowing I have a great place to start and drill down on these great possibilities that present themselves, and if I just follow along my criteria that you have instilled in me, we should be sailing together on a world cruise in a few years. *I'm very happy to have found you,*" **— ****T. Swan**

"*There are very few people I trust enough to take their blanket recommendations....that is why this is so helpful..... learning to cherry pick the best trades and to run trailing stops or **hedge using appropriate shorts .......*" **— ****RR, California (Retired Radiologist)**

**Doc Brown Delivers Stories Others Are Afraid to Touch**

If you look at my research you can see why the Wolves of Wall Street would like to **silence **me. My work shows that every penny spent on investment newsletter advice is money flushed down the **toilet**.

That is because those who can make **money **in the market won't bother with the technical problems of running an investment newsletter. Newsletter **editors **who make enough writing an investment newsletter do so because they can't make money in the market.

And that is just what the **newsletters **are trying to get you to do what they say when they write “*buy this*" or “*sell that*." Here is an actual **line **that just hit my mailbox,

“*The true story of how this trader turned $2,000 into $10 million from his kitchen table, in 9 months*." Don't for a moment believe this **lie**.

If these **marketers **can get you to take action in your trading account they know one thing for certain.

It will be a **snap **to get you to buy their next dud of an expensive annual fee investment newsletter, $5,000 course or $20,000 boot camp — glossed up with fancy promises and fancy sales copy writing. These marketers make their money selling shiny ideas **without **regard to the true returns underlying each strategy.

The underlying economics of the newsletter industry I reveal to you is quite **bizarre**.

Investment newsletter subscribers **lose **millions every year investing in bad ideas. Investment newsletter publishers make **millions **in annual subscription fees.

But now I have uncovered the **ultimate **lie from the Wolves of Wall Street. This investment fib truly pukes up losses of **scandalous** proportions.

**Which Option Strategies Are Tailor Made For Those Born to Lose?**

If you have ever been interested in options there are a few strategies you must immediately become aware of to avoid like the **plague**. These fundamental options trading techniques are guaranteed to **lose **straight out of the barrel.

And they form the basis for **compound **option trading strategies that expose investors to very big losses. Why are these strategies so **popular **among brokers as well as newsletter editors?

Compound option strategies don't just cause complex **losses **they also kick out vastly larger brokerage fees.

But the true returns to investors of these **strategies **have been so hard to calculate that it was impossible to “*prove*" the danger to investor accounts. So it was easy for investment newsletter marketers to falsely claim that these **horrific **options trading strategies actually made money.

Until **now**!

A seminal option trading article came out last year in the #1 ranked **Journal of Finance**. This probing study proves that most **strategies **touted by the financial media are a sure ticket to the poor house. And the Wolves of Wall Street are biting their nails in hopes that you never learn the **truth **that emerges from this article.

**Watch Advanced Training 2 — Stock Options as Lotteries**

The research is so full of “**rocket science**" **math **that the true meaning has never been revealed to the public — until now by me to you. This cutting edge **research **proves beyond a shadow of a doubt that only one of these options strategies is a winner.

**Buying**index and ETF options.**Selling**Index and ETF options.**Covered Calls****Put Selling**- Short Expiration
**Call** - Short Expiration
**Put** **Protective Put****Bull Spread****Bear Spread****Iron Condor**Spread**Butterfly**Spread- Deep in the Money Far Expiration
**Call** **Straddle****Strangle**

isn't that **crazy**?

Only one of the **strategies **above is a winner?! Can you guess **which**?

Most option strategies c are outright **disastrous **or produce mediocre returns to the investors who try them.

One **strategy **alone on the list above actually stands to make investors big money. Do you want to know **which**?

It truly is the **one perfect option strategy**. Enroll **now **and here is what you get…

This course **teaches **you how to trade the one — perfect — option strategy. I take you by the hand and **mentor **you through each step of my unique ultra-high beta controlled leverage long term investment process.

**Introduction 1 — The Option Mechanics Toolbox Every Savvy Stock Investor Must Master**

**Benefits **to you …

- Laser impress
**permanently**into your mind the precise mechanics of exercise and strike. - See why
**index**options can be very different beasts from plain vanilla stock options. - Marvel at the modern American invention of the
**derivative**. - How options derive their value from underlying
**investments**. - Watch as I
**reveal**to you how the option price is derived from the underlying. - Grasp the power of extrinsic time value above and beyond
**intrinsic**option premium price. - Develop a strong sense of
**moneyness**. - Utilize payoff diagrams for serious real money
**campaigns**. - See how a covered call is the same as a bank deposit, a call and a
**short**stock. - Employ a time decay chart to clearly see your best option bets for maximal
**probable**profits.

**Introduction 2 — Basic Option Pricing with Binomial Outcome Trees for Valuation!**

More **benefits **to you …

- Model option value on
**expiration**date. - Calculate the hedge ratio also known as
**delta**. - See how option premium changes for each unit rise of
**underlying**stock. - Grasp how options trade in a parallel yet
**connected**universe with equity markets. - See risk neutrality as a special case of certainty
**equivalence**. - Marvel at how call option
**payoff**is zero in the binomial down state. - Reintroduce yourself to
**Euler's**number from high school math. - Create a pyramidal
**matrix**of possible share prices. - Use the risk free rate of
**return**to model forward up and down share price movements. - Plug
**probabilities**of a rise or fall into the binomial model.

**Introduction 3 — Black Scholes Option Pricing Theory and the Real World Impacts!**

Even **more **benefits …

- Recognize the five key variables Fischer Black and Myron Scholes used to model option pricing.
- Utilize the knowledge of how fluctuations of the underlying stock influence the price of puts and calls.
- Know when underlying volatility is pumping up option values.
- Wonder at how increasing interest rates actually increases call values but hammer put prices.
- Employ the VXN to compare the implied volatility of the NASDAQ to that of any other stock market index.
- Grasp the value of a call as the share price less a bank loan.
- Blaze into your mind via a time decay chart the reality that the farther out in expiration an option is the more valuable it becomes.
- Derive year fractional expiration as days remaining divided by 365.
- Value any call as delta times the underlying share price less a bank loan.
- Repulse at how warrants gifted to fat cats dilute your ownership share in private placement investments.

**Introduction 4 — Real Options Offer Insights Into Your Real Estate Investments!**

Yet **still **more benefits …

- Analyze the choice of two real estate option projects under high and low demand.
- Consider the real option case of oil tankers that can be mothballed when unprofitable.
- Reflect on the combination-turbine electricity market from a real options perspective.
- Ponder how large aircraft assembly firms streamline sales with real options.
- Peruse a graph that proves that the NPV of a real option decision to purchase an expensive asset is about zero with long time to delivery.
- Why real options are rarely available in practice.
- See how real options apply to pharmaceutical share pricing as firms move through consecutive FDA approval trails.
- Examine how real options can change underlying pricing conditions.
- Build your understanding of how real estate options can help you.
- Strengthen your economic intuition with knowledge of real options.

**Enjoy the Advantage of Superior Information**

And this is just a **smattering **of the total benefits of this program.

If you **enroll **right now you get the best option training on the web today. To get the same quality of options trading training anywhere else would cost you **$185,052** in elite MBA mentoring at a school such as **New York University Stern** or **Harvard** Schools of Business.

To enroll now mash that rectangular blue **button** to the right up there. It has these words “*Take This Course.*"

Invest some of your **PayPal **electronic pocket change towards a brighter financial future!

**-Scott**

**Dr. Scott Brown, ***Associate Professor of Finance of the AACSB Accredited Graduate School of Business of the University of Puerto Rico*

**P.S. ***This is a risk free offer. Udemy extends to **you a 30 day money back guarantee.*

Who is the target audience?

- This course is for equity investors seeking advanced training in stock options.

Compare to Other Stock Options Courses

Curriculum For This Course

7 Lectures

01:33:21
+
–

These 4 Lectures Cover the Nuts and Bolts of Option Trading Starting from Basics
4 Lectures
01:07:04

A **call **option allows you to buy the underlying stock or futures or currency contract for a pre-selected strike. The **strike **is also called the exercise price. **Exercise **is only allowed on the expiration date in the case of a European style option. You can exercise on or before the expiration date of the option in the case of an **American **style option.

**Some Index Options are European Style!**

A **put **option allows you to purchase an underlying stock, futures or Forex contract at a set level also known as the strike or exercise price.

Option **buyers **have the right to purchase — in the case of the call — or sell — in the case of a put. But the **purchase** of the call or put does not carry with it the obligation to buy or sell.

However, the **seller **of an option — the writer — does have the obligation to sell — in the case of a call — or buy — in the case of a put — the stock, futures or Forex contract underlying the deal.

A call, put, futures or Forex contract is a **derivative**. These are financial **assets **created from other financial assets.

In this case the call or put is **derived **— created — from the shares of stock, futures contract or currency forward contract that underlies the option. For that reason the asset from which a call or put is created is termed as the **underlying **stock, or underlying futures contract or underlying forward contract.

The option **premium **is the price paid for an option — call or put. This also called the option price.

The option **price **is derived from the underlying.

**The Intrinsic Value is Your Lifeboat in Raging Equity Seas!**

The **intrinsic **value of a put or call option is the difference between the strike price and the underlying asset price — 100 shares of stock, a single futures contract or a single currency forward contract.

Time premium is also known as the **extrinsic **value of an option. This is the value of the option in **excess **of the intrinsic value.

The price at which the **underlying **asset can be bought or sold is termed the exercise price. This is also known as the strike price.

The last day within which an option can be exercised is known as the expiration **date**. An American **style **call can be exercised at any time up to the expiration date of the put or call option.

A **European **option on the other hand can only be exercised on to the expiration date. You are most likely to see these in the form of equity **index **options.

The option value at expiration is a **function **of the stock and strike — exercise — price. I give you the **example **of a stock call and put option with a strike — exercise — price.

I walk through **quotations **of stock options — that I have personally profited from.

This allows me to show you that the value at expiration for a call option is **zero **if the stock price is less than the exercise price at expiration. Conversely I show you that a put option is **worthless **if the stock price is greater than the exercise price at expiration.

The call option has **value **if the stock price is greater than the exercise price. The **formulation **of that value is;

**Rule 1 — The Call Intrinsic Value = Stock Price – Exercise Price**

The put options has worth if the stock price is less than the exercise price at expiration. This formulation is; stock price < exercise price.

**Rule 2 — The Put Intrinsic Value = Exercise Price – Stock Price **

Each of these **ideas **are explained with actual numerical examples.

For instance the value at expiration in the first example is that if the stock price per share is less than the exercise price of per share than the call value is zero since it is **out-of-the-money**.

The next examples shows you that if the stock price is greater than the exercise price of then the call value is **equal **to the stock price less the exercise price. This is valuable since the call is **in-the-money**.

If the stock price per share is **greater** than the exercise price per share the put is worthless because it is out-of-the-money. But if the stock price falls **below **the exercise price the put value is equal to the exercise price less the stock price and expires in-the-money.

Then I move on to explain the inner workings of a call option position **diagram**. This is followed by the explanation of a put option **position **diagram.

Controlled leverage option investors are most interested in **payoff **diagrams. These **incorporate **the initial cost of the option into the payoff.

In the payoff diagram you will discover that the **profit **to a call buyer is a loss to the seller. Investors who **write** — sell — calls have unlimited potential for loss. Then you will see that the **seller **of a put option has a loss limit of the stock becoming worthless.

**Deep in the Money Six Month or Longer Expiration Calls Are Your Best Equity Option Investment!**

But that amount can be a larger loss than the premium **garnered **at the sale of the option.

The profit diagram is useful for **analyzing **the profits of any option transaction. This helps us visualize the **timeline **of cash flows.

The call **buyer **loses money if the stock price is below the exercise price. But as the stock price increases the profit potential of the call is **unlimited**.

Remember this important fact regarding **long **calls; they are the best option investment.

Then we **dissect **the profit diagram for the seller of a put. The put writer will profit if the stock price is above the **break-even **price.

The break-even point of a put write **transaction **is the exercise price less the price of the put option. The potential profit to a put seller is **limited**.

Remember this important fact regarding **selling **options. The profit to option **writers **is harshly limited.

The profits to a call buyer are **unlimited**.

Next I give you conclusive **evidence **that buying a stock and selling a call is not a good strategy. The **short **call wipes out any upside profits to the stock.

**Downside **movements wipe out value on both sides of the transactions.

**Avoid Investing in Covered Calls, Out of the Money Calls, Put Selling and Protective Puts!**

The covered call is a very **poor **investment strategy. In an upcoming lecture I will show you why out of the money **short**-term expiration calls are even worse.

Also **bad **is the strategy of put selling.

And **protective** puts are bad too. They have been shown to be much **overpriced **forms of insurance against downside drops in your single stock positions.

This is the **combination **of buying both a stock and a put option.

This is a **long **simultaneous position in the stock and a put. The loss due to the fall in the stock price is exactly **offset **by gains in the put price.

This strategy protects the **individual **retail single stock investor from loss due to a fall in the stock price. But this **preserves **the gains if the stock price increases.

Many investors **scramble **after this as it is touted as insurance against falling stock prices.

Recent top level financial research has revealed the **premium **needed to purchase these protective puts is grossly overpriced and dissipates the benefit of the insurance component of this highly popular strategy.

At the end of the day I am sure you will **conclude **that the deep in the money long expiration call is the best option investment in equities.

**Why Straddles and Strangles Are Nasty Option Investments**

A straddle is **formed **with the purchase of a call and a put at the same strike and expiration. A closely related method is a **strangle **where the strikes are above and below the underlying price.

Option investors attempt to extract profits via straddles and strangles when stock price **volatility **is high.

These too have been shown to be **overpriced**. This means that the gains to one side of the straddle or strangle are **consumed **by the losing leg.

Then I walk you through three **payoffs**.

You can buy a share of stock where you gain or lose as the **stock **price rises or falls. Another payoff is presented where there is no **downside **— even if the stock falls you retain your initial capital. Then I show you a third **lose-lose **payoff where the stock investor loses if the stock price falls and loses if it rises.

The lose-lose strategy can be replicated through a **covered call** created through the purchase of 100 shares of stock and the sale of a call option against that very same stock.

It may seem **strange **that I spend so much time carefully showing you how to create a lose-lose investing scenario. But this allows me to prove to you that a covered call is equivalent to a **bank deposit** plus the purchase of a call and shorting stock.

This allows you to **replicate **the purchase of a put.

**Put-Call Parity is your Key to the Option Kingdom**

This is proof of a very important **concept **we will use later for the Black Scholes option pricing model. This leads to put-call parity first delineated by **Vanderbilt **finance professor Hans Stoll.

Then I show you how the option contract **specifications **can actually shape payoffs through the sale and purchase of two calls. The example is given with a **CEO **not likely to influence share prices outside of a narrowly defined range.

The **time decay chart **allows you to see how the option price drops as the time to expiration nears.

This allow us to **map **out how increases in the underlying stock price, underlying stock price volatility, time to expiration and discount rate increase call values. **Increasing **the strike price decreases the value of a call but pushes up the price of a put.

Increases in **underlying **share prices or discount rates drop put values.

This allows me to show you that the upper **limit **on the value of a call is the stock price. The **lower **limit is either zero or it is the difference between the stock and exercise price.

This allows you to conclude that the two primary **determinants **of option values are the strike — exercise price and the stock price.

I show you a **diagram **of two stocks. One has higher **volatility **as measured by a probability distribution with a higher standard deviation of stock returns.

You will see that the higher the **standard deviation** — volatility — of underlying stock returns the higher the premium cost of the call or put option. This can be shown in terms of **linear **payoffs.

**How Underlying Stock Return Volatility Pumps Up Option Prices!**

This is a very important characteristic of options that **distinguish **these derivatives from other financial securities.

A volatility chart shows that the standard deviation of underlying returns **impacts **option value in much the same fashion as time to expiration. This can be seen by comparing a **volatility **chart with a time decay chart.

As volatility increases option **value **increases. As time to **expiration **increases option value increases.

We will **dissect **the pricing characteristics of a call option. I will show that an **increasing **stock price increases the price of a call option. Decreasing the **exercise **price drops the value of a call option.

An increasing **interest **rate increases the value of calls. Increasing the **time **to expiration and the volatility of the stock price — sigma — increases call premium for the same option.

The **upper **bound of the option price is always less than the stock price. The lower **bound **of the call price never falls below the payoff to immediate exercise. This is the stock price less the exercise price of zero whichever is **greater**.

If the stock is **worthless **so is the call. As the stock price increases **dramatically**, the call price converges to the stock price less the present value of the strike price.

Finally we analyze the situation of a **manager **who has been offered the CEO position of two firms. Both offer options in executive bonus **compensation**.

The exercise price and maturity are **identical**. The current stock price of each firm is the **same**.

There is but one difference between the two **employee stock option** packages — ESOs. The **underlying **volatility — in terms of standard deviation which is also termed as sigma — of the first firm is lower. That of the second is **higher**.

Based on the discussion in the lecture video and the text above the manager should conclude that the firm with higher underlying firm **equity **return volatility offers the highest value for the manager.

Preview
17:20

**Super Simple Option Valuation**

The **binomial options pricing model **is an iterative method for precisely describing the price of any option developed by three highly influential finance professors in 1979. These are Professor Mark Rubinstein of the **University of California at Berkeley **and Professors John Cox and Stephen Ross of the Sloan School of Business of the **Massachusetts Institute of Technology**.

- Cox, J. C.; Ross, S. A.; Rubinstein, M. (1979). "Option pricing: A simplified approach". Journal of Financial Economics 7 (3): 229.

The binomial model works with each base unit of **underlying **stock movement. These base movements have just two **outcomes** at each stage; up or down. The value of a stock in a down **state **and up state is given in a simple example.

The **corresponding **option value on the expiration date is then explained.

The example continues with the **assumption **that the stock investor owns just about half a share of stock and also borrows the present value of the remainder of the state value in the case of a drop.

This **leads **to a value of 0 if the stock drops to $320 or $100 if the equity share price rises to 500.

These two payoff scenarios allow us to calculate **delta**. This is the **hedge **ratio.

It tells you how much the option value will increase for each unit rise in the underlying share price in the case of a call — or premium reduction in the case of a **put**.

You will discover that this vastly important number — for **controlled leverage** option investors — is easy to calculate. The option delta is simply the spread of possible option prices **divided **by the spread of possible share prices.

You will use the concept of **delta **throughout this course. Please make sure you take the time now to fully **understand **it.

Options trade in a **parallel **market derived from the underlying share price. This means that the **law of one price** says that arbitrage will kick option prices back in line .

Surprisingly this process is **independent** of firm economics of the underlying stock — since the option price is given — derived from the underlying.

Hence **arbitragers **can be assumed as risk neutral. This allows us to derive a simple binomial outcome within a **risk neutral** framework. Risk neutral is a special case of **certainty equivalent**.

I then show that the expected return to call option **arbitragers **is equal to the risk free rate of return.

**Expected **return is equal to the probability of a rise times the magnitude of a possible up move plus one less the likelihood of a rise times the size of an estimated down move. That's is equal to the **risk free rate**.

The magnitude of up or down moves in the underlying stock is related to the **volatility **of equity returns. This is measured by standard deviation termed **sigma**.

Then I show you that a put option can be **valued **with the same approach. I start by showing you two possible **terminal **values for each case.

Once you know the **likely **price moves for an iteration you must calculate delta. You will **sometimes **see delta denoted by the letter h.

This symbolizes the fact that delta is also termed the **hedge **ratio.

The binomial option pricing model of Cox, Ross, and Rubenstein requires that you sell shares and **lend **the proceeds. This allows you to **price **the option.

Then I **walk **you through an example with three nodes. Those **nodes **are now, month 3 and month 6.

This **illustrates **possible present and future values of a stock.

Then I work you through the math to calculate the option **value**. I give you the direct **measure **of the probability that a stock will rise.

This is **calculated **as the ratio of the risk free interest rate less the size of a downside change and the upside change less the downside change.

This is easily plugged into the **valuation **formula. Remember that the binomial model valuation formula is the probability of a rise times the associated option payoff in that state plus the probability of a fall times the associated **payoff **in a drop.

The payoff to a call option in any down state is **zero **since each example begins with an at the money call.

Next we explore the general **formula **for the binomial option pricing model. This is **probability **up = *p* = [*a* – *d*]/[*u* – *d*]. And probability down = 1 – *p*

The term “a” is **Euler's number **to the power of the interest free rate and delta. The term “d” is Euler's number to the power of negative **standard deviation** — sigma — times the square root of the time to expiration expressed as a percent of the year.

Euler's number "e" is a constant equal to **2.71828**

The time to expiration is **denoted **by the letter “h.”

The term “u” is Euler's number raised to the power of **sigma **times the square root of the time to expiration. This **explanation **is followed with a numerical example.

Possible share prices are calculated forward from the present in two **iterations**.

This creates a **pyramidal **matrix of possible share prices forecast into the future. The **value **at each node on the slide is the greater of the present value of the two branches or the intrinsic value.

Once forward looking share prices are established the option values are calculated **backwards **at each node.

Then you will discover that as the time interval is shortened, the binomial model **converges **to the Black-Scholes model. Cutting the time interval creates more steps and more potential price **changes**. **Binomial **price results differ a lot from Black-Scholes value with very few steps.

When you calculate the binomial option pricing model with many steps you get closest to the **Black Scholes Option Pricing Model**. This is shown with a **numerical **example.

Introduction 2 - Basic Option Pricing with Binomial Outcome Trees for Valuation!

14:06

**The Black-Scholes Pricing Model Is Your Option Money Map!**

Your exploration of the **continuous **math option pricing model begins with a review of the components of option prices.

The option price for the Black-Scholes model depends on these five **variables**;

- Increasing
**underlying**stock price increases the price of a call but reduces the price of a put. - Increasing
**exercise**price decreases the value of a call yet increases the value of a put. - Increasing share
**volatility**pushes up call prices but can increase or drop put prices. - Longer times to
**expiration**equate into higher call and put prices. - Increasing
**interest**rates increase call values but reduce put values.

The value of a call is now seen as equal to **delta **times the share price less the bank loan.

In other words the value of a **call **= (delta)(price) – (bank loan). This is equivalent to *N*(*d*_{1})×(*P*) – *N*(*d*_{2}) ×[PV(EX)]. *N*(*d*_{1}) and *N*(*d*_{2}) are pulled from **cumulative normal distribution** tables or from the NORMSDIST(d) Excel function.

**Key Model Variables That Impact Real World Option Prices! **

In order to understand the Black-Scholes option **pricing **model I must define for you the key variables that are inputs into the model.

**Oc**is the Call option price**P**is the Stock price**N(d1)**is the Cumulative normal probability density function of (d1)**EX**is the strike or exercise price.**PV(EX)**is the Present value of strike or exercise price**N(d2)**is the cumulative normal probability density function of (d2)**R**is the discount rate — the 90 day commercial paper rate or risk-free 3 month t-bill rate.**t**is the time to maturity of option — as % of year.**v**is the volatility-annualized standard deviation of daily returns

Next I introduce you to the l**og-normal distribution**. The log-normal distribution is **skewed **to the right.

This reflects the fact that a stock can only drop by a **hundred **percent. But that same stock can **rise **by far more than 100%.

This says that we can expect far more **extreme **profitable movements than we would otherwise expect.

**Expect The Unexpected in Our Log-Normal Stock Markets! **

The variable d1 in this case is equal to the **natural **logarithm of P/X plus t times r plus one half v squared divided by v times the square root of t. Once this is **crunched **d2 is calculated as d1 less v times the square root of t.

Then I work you through a numerical example where t should be **expressed **in years — time to expiration divided by 365 days in a year — and r is a decimal plugged-in the formula.

Then *d*_{2} and *N*(*d*_{2}) are **calculated **in the second step. The option price is **calculated **and you will see that it is a fraction of the stock price.

I show you how this maps into the time **decay **chart. This shows you that the option price we calculated **declines **as the time to expiration drops.

We work through another problem for **practice**. Once again you will see that the value of a **call **= (delta)([stock price) – (bank loan) = *N*(*d*_{1})×(*P*) – *N*(*d*_{2}) ×[PV(EX)]. Here PV(EX) = (EX) (*e*^{– (r) × (t ) }) is calculated with the **continuous ****time discounting formula**.

**Other Option Topics That are Interesting to Value and Private Placement Investors — ESOs and Warrants!**

Then I show you how to calculate the call values for two different managerial **employee stock option **— ESO — packages. With Black Scholes pricing values the **correct **choice becomes clear — all things equal.

The next important tool I introduce you to is the **VIX**.

This indexes implied volatility fluctuations on in and out of the money **SPX **puts and calls trading on the S&P futures contract. But I don't stop there. I also show you how to measure volatility fluctuations on the NASDAQ using the **VXN**.

Then I show you have **Put – Call Parity **can be used to calculate the put price given the call prices we just calculated. The put price = *O _{C}* + EX –

There are many **variations **of pricing models for options,

**American**calls with no dividends**European**puts with no dividends- American
**puts**with no dividends - European
**calls**and puts on dividend-paying stocks - American calls on
**dividend**-paying stocks

Next we revisit the **convergence **of the binomial to the Black-Scholes model. When few steps are used the binomial outcome will **differ **more from the Black–Scholes price.

But the numbers are **close **after 100 steps.

The final topic of this discussion is to show you that the exercise of a **warrant **increases the number of shares outstanding. The **dilution **factor reflects that fact.

Introduction 3 - Black Scholes Option Pricing Theory and the Real World Impacts!

17:14

There are four types of **real options**. This **includes **the;

- option to
**expand**. - option to
**wait**. - option to
**trim**down or**abandon**. - option to
**vary**the mix of output or the firm's production methods

The value of a real option is the project **NPV **with the real option less the NPV without the real option.

What can we do with negative NPV **projects **that might possibly become big turnarounds? I walk you through an NPV analysis with a **negative **value.

But the project offers **management **the option to expand into an industry that may also expand in profitability. If the industry expands in profitability the NPV of the project would become **positive**.

These insights allow us to value a **call **option on a negative NPV project.

We have to consider the forward **distribution **of possible present values. These present values are assumed to be **log-normal **in distribution.

Log-normal distributions are **skewed **to the right.

This means that expected outcomes can be far greater than the most **likely **outcome on average. The most likely **average **— or **median **— outcome is at or near the highest point on the probability distribution graph.

The **distribution **shows a wide range of possible present values for the negative NPV project in future years. It shows the expected **value **where the option to invest pays off in the shaded area of the chart.

The option to **wait **is graphed next. The call option is more valuable the **longer **the wait. That is as long as a **competitor **does not catch up with the idea.

Then the option would have a lot **less **value. The longer the wait, the **higher **the real option value sans same project competition. The time **premium **is the value of being able to wait.

**Option Value = Intrinsic Value + Time Premium**

We can obtain the option to wait and invest later only if there is high **demand**. Take the choice of two different **commercial **real estate projects.

Take for instance the opportunity to develop either a **corporate office building** or a **small hotel** on vacant land the firm owns.

This is a very **difficult **choice.

What if another investor builds the same structure **nearby **while you wait? The cash flow **potential **would be much diminished.

The area in the development option graph below wait would **reduce **drastically.

Real options can be extended to temporary **abandonment **in a graph I present to you as evidence. Imagine these outcomes for oil tankers that could be **mothballed**;

- If the maritime shipping
**rate**is less than R then reactivate the tanker - If the maritime
**shipping**rate is less than M then mothball the tanker

These are reasonable **temporary **abandonment rules.

How about **combination-turbine** electricity from natural gas plants? I show you a graph of how the price of **electricity **in the United Kingdom spikes from time to time.

If you owned a combination-turbine plant you could turn it on when electricity prices **spike**. Sure enough these operations **run **about 5% or the time.

But how the heck do you **value **an operation like that if you want to invest in one? I'll show you how the investor ends up with a call **option **to produce power where the strike is the cost it takes to run the plant.

Big aircraft companies like **Boeing**, **Embraer **and **AirBus **pre-sell by writing corporate covered call real options on their sky vessels.

The option **buyers **are airlines interested in purchasing aircraft. Airline buyers gain the ability to get a lower price or **guarantee **the delivery of the aircraft without the obligation to purchase. There are other **industry **specific conditions.

The option if exercised in **year **three, option guarantees fixed price and delivery at year four, for instance.

Managers in AirBus do not have the same risk as a covered call writer in the **secondary **equity market. That is because the firm is producing and selling to another firm the underlying asset; the **passenger **jet.

A **Main Street** investor engaged in covered calls has to come out of pocket for the full cost of the underlying asset. For this reason the covered call strategy is very bad for the **individual **retail investor.

But a covered call in real options allows a buying — consuming — and selling — producing — **fortune 500** firm work out a deal on a very large financial transactions otherwise not possible. This stimulates **sales **for the aircraft manufacturer.

And competitors don't get the **shaft **as easily in adverse market conditions.

**Without **the option, the plane can still be ordered in year three but with an uncertain price tag and delivery terms into year four. A real option to purchase a jet liner **reduces **the uncertainty of negative cash flows associated with the initial investment in a new passenger plane.

I will show you a graph that describes why the real purchase option is worth the most when the NPV of the decision to purchase now is about zero and the **forecast **wait for delivery is a long way out in time.

**Pharmaceutical **forward cash flows are best described with real options to estimate the firm's present value of growth opportunities. New medical compounds are very hard to pass through the **Federal Drug Administration**.

There exists a series of **FDA ****trials**.

If **phase II** trials succeed there is a recall option to invest more. If exercised, there is much higher chance of launching approved drug. The present value of the drug, **forecast **in year five is the underlying asset of the real call option to the firm and its shareholders.

Real options often are not available in **practice**.

And even when **accessible **real options can be complex and offer no exact answer. A lack of **clear **structure of operational or tactical path and obfuscated state contingent cash flows can confound the real option pricing process.

And the problems with real options don't **stop **there. The firm's **competitors **also have real options.

Real options of other firms change the **underlying **pricing conditions and the nature of the industry used for valuation. This training will help you understand how to get a better **deal **if you invest in or write real options.

But, if you are like most Main Street investors you will **likely **never purchase or sell real options. But this unique perspective will make you a much better stock, futures or currency option trader by sharpening your derivative **intuition**!

Introduction 4 - Real Options Offer Insights Into Your Real Estate Investments!

18:24

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Quizes
0 Lectures
00:00

Challenge 1 - An Option Mechanics Toolbox Every Savvy Stock Investor Must Master

10 questions

Challenge 2 - Basic Option Pricing with Binomial Outcome Trees for Valuation!

10 questions

Challenge 3 - Black Scholes Option Pricing Theory and the Real World Impacts!

10 questions

Challenge 4 - Real Options Offer Insights Into Your Real Estate Investments!

10 questions

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Doctoral Level Training Show Exactly Which Option Investments are Bad or Good!
3 Lectures
26:20

**Columbia University Study Shows Implied Volatility Fluctuations Forecast Equity Returns!**

Get this insider trick to spotting stocks on the rise by watching the implied volatility levels of **calls**. Track **puts** for your crystal ball to stocks on the brink of collapse from “The Joint Cross Section of Stocks and Options.” This cutting edge options study is from **Columbia**, **Georgetown** and **Fordham** University Professors Beyong-Je An, Andrew Ang, Turan G. Bali and Nusret Cakici.

**Reference:**

- An, Beyong-Je, Andrew Ang, Turan G. Bali and Nusret Cakici. 2014.
*The Joint Cross Section of Stocks and Options.***Journal of Finance 69(5)**. 2279-2337.

**Background: **

Prior studies have used high-frequency intra-day or daily data to measure a **lead-lag** effect between option and stock markets. These older studies show that options and stocks are **fairly** priced over very short term time intervals.

This new study finds that option implied volatility **predict** the cross section of stock returns. Stock returns also predict **future** option volatility. Both of these findings run **counter** to predictions based on the original Black-Scholes pricing model.

**Model:**

The **intuition** behind the model is that informed traders will trade the stock and option markets interchangeably and simultaneously. The amount of trading is contingent to the level of **noise** in each market.

A **dealer** stands ready to arbitrage thus linking the stock and option markets.

The market moves on the trades of the marginal **informed** investor. But the information from informed option trading does not fully adjust in the stock market to a fully revealing rational **expectations** economy.

This allows for **predictability** from option prices to stock returns and vice versa. Periods of high demand from noise trading increase this **predictability**. The two closest related models are those of **Easley, O'Hara and Srinivas [1998]** and that of **Garleanu, Pedersan, and Poteshman [2009]**.

**Hypothesis:**

The first hypothesis that emerges from the **model** is that option volatility can predict future stock returns. The second hypothesis is that this **predictability** is highest with high underlying stock – and option – volume.

The third hypothesis is that **informed** trading gives rise to stock level information predicting option returns.

In other words there is **simultaneous** predictability between both markets; stock and options. Their fourth hypothesis is that past stock returns predict future increases in option volatility and impending weakness in underlying stock returns.

**Data:**

The data is obtained from the **Ivy OptionMetrics** database. **Portfolios** are created on the first trading day and the second Friday of the month. **Variables** include the underlying stock price, time to maturity, strike, and price of the option as well as volume and open interest.

**Table 1** shows the descriptive statistics of data.

There are **1,261** option-able stocks per month in 1996. This rises to **2,312** stocks per month by 2011. Call and put implied volatility is the highest in 2000 and 2001 during the centennial **crash**. The most recent crash in 08' and 09' denoted a period when **CVOL** and **PVOL** implied volatility increased from about 40% to 60% respectively.

**Methodology:**

The construction of variables is listed on page 2284. These **include** Beta, Book to Market, Momentum, Liquidity, Short-Term Reversal, Implied Volatility Innovations (ΔCVOL and ΔPVOL), Call/Put Volume (C/P Volume), Call / Put Open Interest (C/P OI), Realized Implied Volatility Spread (RVOL-IVOL) and Risk-Neutral Skewness (QSKEW).

Portfolios are **sorted** on ΔCVOL and ΔPVOL.

**Bivariate** portfolio sorts are studied for long term predictability by constructing overlapping holding periods following the methodology of Jagadeesh and Titman (1993). A **Fama McBeth** cross-sectional regression analysis is performed using the Newey West (1997) t-statistic for significance of findings.

**Results:**

The key results are,

- Stocks with large increases in call implied volatility predict future
**increases**in share price. - Stocks with large increases in put implied volatility predict future
**decreases**in share price.

**Table V** reports the long-term predictability results of the study. The risk-return adjusted and average return **differences** from low to high ΔCVOL are statistically significant for one to six month time frames.

The **predictability** of ΔPVOL persists for up to three months. Thus the predictive effect of large increases in implied call volatility is of higher intensity and longer **duration** than in the case of the imputed volatility of puts.

Panel A of table VI shows that the mean slope of the ΔCVOL **coefficient** is 1.57. The associated **t-statistic** is 3.13. The **average** slope coefficient of ΔPVOL is -1.85 with a t-statistic of -3.78. Thus the effect of large changes of implied volatility in call pricing correctly **forecast** with high statistical significance positive Jensen's Alpha in the underlying equity in a Fama-McBeth Cross-Sectional Regression.

Many **underlying** variables that impact the cross section of stock returns impact the implied volatility of options.

Forward **spreads** of about 1% per month arise from decile ranked implied volatile portfolio sorts. These returns **persist** for up to six months. This is **consistent** with informed participants arriving to the option market before movements occur in equities.

Implied option volatility is shown to forecast the cross section of **stock** returns. Conversely, firm level **characteristics** such as momentum, value (book to market) and liquidity are shown to impact option implied volatility.

**Lagged** excess stock return is a particularly strong prediction variable for implied volatility changes in both calls and puts. Increases in **call** option implied volatility predict high underlying stock returns over the following month.

Increases in **put** option implied volatility forecast poor stock returns into the following month. This relationship is especially strong for puts with implied volatility that moves **against** the direction predicted by put-call parity.

The **persistence** over time and economic strength of the underlying share return predictability from call and put implied volatility is "*remarkable*." The lead-lag option-stock relationship is statistically very **strong** and economically large. This is because the change in levels of implied volatility is a simple **measure** of the arrival of new option investors.

This is **strongest** for the next month but persists up to 6 months forward.

**Decile** portfolios of stock spreads relative to past fluctuations in call implied volatility exhibit returns of about 1% per month in raw return with similar Jensen's Alpha in multi-factor CAPM models. Results for put options generate spread returns greater than 1% percent per **month** within the most extreme spread deciles.

The second reason that this result is **fascinating** is because many common market strategies have reversed sign or weakened during the 08' and 09' crash. Yet this lead-lag option implied volatility underlying return relationship **continues** through and into the most recent data.

This result is consistent with **models** where informed traders enter first into the option markets. See **Chowdry and Nanda (1991) **and** Easley, O'Hara and Srinivas (1998)**. Stocks with **abnormal returns** of 1% relative to CAPM tend to show an increase in call (put) implied volatility over the next month of 4% for calls and 2% for puts.

Informed trading partially adjusts prices, this resolves future uncertainty of firm cash flows. Option open interest is shown to be highly **correlated** with implied volatility.

Finally I show you where to **access** implied volatility charts of any stock with traded options.

**Additional References:**

- Chowdhry, Bhagwan and Vikram Nanda (1991)
*Multimarket Trading and Market Liquidity*.**R****eview of Financial Studies 4 (3).**483-511. - Easley, David, Maureen O'Hara and P. S. Srinivas. 1998.
*Option Volume and Stock Prices: Evidence on Where Informed Traders Trade*.**The Journal of Finance 53(2)**. 431-465. - Garleanu, Nicolae, Lasse H. Pedersen, and Allen Poteshman. 2009.
*D**emand-Based Option Pricing*.**The Review of Financial Studies 22(10)**, 4259-4299. - Jagadeesh, Narisiman and Sheridan Titman. 1993.
*Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency*.**The Journal of Finance 53(5)**. 63-91. - Newey, Whitney and Kenneth West. 1997.
*A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix*.**Econometrica 55(3)**. 703-08. - Fama, Eugene, and Kenneth French. 2012.
*The Cross-Section of Expected Stock Returns*.**The Journal of Finance 47(2)**. 427–465.

The Joint Cross Section of Stocks and Options by a Top Columbia Business School!

11:16

**Top Scientific Study Proves Selling Puts (or Covered Calls) to Be Very Bad Idea!**

And the **bad **news doesn't stop. Buying **out of the money options** are shown as the worst investments on Wall Street. The clear lesson is that deep in the money late expiration calls are best **investments**.

**Reference:**

Boyer, Brian and Keith Vorkink. 2014. *Stock options as lotteries*. **Journal of Finance 69(4).** 1485-1528.

**Background:**

Individual investors have been shown to routinely make losing **investments**. See **Kahneman and Tversky (1979) **and **ODean (1998)**. Certain lottery-like option strategies such as** buying out-of-the money short term expiration calls **are known to be losing investments. Prior studies have shown losses to **lottery-like** option preferring investors to be in the **magnitude** of 12% per year on out-of-the money call options.

This study shows **losses **to as high as 50% per week.

*Hypothesis:*

**Out-of-the-money** options are losing investments.

**Data:**

The data is obtained from the Ivy **OptionMetrics **database. **Portfolios **are created on the first trading day and the second Friday of the month. **Variables **include the underlying stock price, time to maturity, strike, and price of the option as well as volume and open interest. This **covers **194,822 option quotes over 24 portfolio dates per year.

*Methodology: *

Returns are calculated and a Newey West (1997) t-statistic is used to test if the differences are equal to zero. CAPM is used to measure pricing errors. Fama-McBeth regressions are utilized.

Results: Out of the money options exhibit more return skewness than in-the-money options. In fact, in the money options exhibit almost no skewness.

Moneyness is defined as the strike price divided by the stock price (X/S). The deepest in-the-money call would have moneyness of zero. The farthest out of the money put would have a moneyness of zero.

shows skewness as a function of**Figure 1****moneyness**for calls and puts. Out-of-the-money options are the most heavily skewed.shows that the magnitude of the impact of volatility on**Figure 2****skewness**is mediated by maturity and moneyness. Moneyness of**X/S**= 0.9 is a in the money call option where high underlying volatility leads to just sightly higher skewness. But higher underlying**volatility**leads to less skewness for 0.9 moneyness out of the money put options. High**underlying**volatility leads to lower skewness for out-of-the-money call options.

Skewness increases with **maturity **for in the money options. It **decreases **with out of the money options.

Moneyness nearly fully **explains **skewness. In the money **options **are virtually devoid of return skewness. After that the **second **most important variable to explain option return skewness is underlying volatility.

shows that skewness increases over**Table II****quintiles**by construction. For example**seven**day to expiration call option skewness ranges from 0.40 to 29.94.hows that average bid-ask spreads are large and increase with increasing skewness.**Table III**sshows that returns decrease sharply across skewness bins and especially among the shortest expiration options.**Table IV**shows that CAPM alphas decrease across skewness quintiles.**Table V**shows that large differences in CAPM alpha across option return skew quintiles is not driven by underlying stock characteristics.*Table VI*shows that low average option returns cannot be explained by co-skewness or volatility risk.**Table VII**shows that ex-ante skewness and expected option returns are related. This relationship is independent of underlying risk factors.*Table VIII*shows large spreads in alphas between portfolios of low versus high skewness.**Table IX**indicates that total skewness is priced.**Table X**reveals that option writing investors who sell either puts or calls earn CAPM alphas that are statistically insignificant and indistinguishable from zero.*Table XI*

Hence any investors who pays to learn to write options is surely losing on their put selling **premium **income "*investment*." The premiums that investors pay to buy out-of-the-money options with high ex-ante skewness are not passed on to **option writers**.

All out-of-the money **portfolios **exhibit negative returns to buyers. Positive **returns **are only associated with in-the-money options for investors buying options. **In-the-money call** portfolios are shown to offer higher returns than in-the-money put portfolios.

Large differences in option portfolio CAPM **alphas **between out-of-the money and in-the-money option portfolios are not attributed to differences in underlying stock characteristics. Out-of-the money options are consistently shown to offer **poor **returns to investors. The study shows that the vast **majority **of option buying [selling] is at the ask [bid] of very wide spreads. Worse yet over **hopeful **investors are shown to rush to buy options incurring losses of up to 50% per week due to astronomically high costs incurred from transacting at the extremes of these wide spreads. They do this to gain **exposure **to out-of-the money options with high lottery like payoffs.

**Losses **incurred by out of the money option buyers are not recovered by covered call or put sellers. These sellers are investors who write options.

*References:*

- Kahneman, Daniel and Amos Tversky. 1979.
*Prospect Theory: An Analysis of Decision under Risk*.**Econometrica 47(2),**263-291. - Terrence Odean. 1998.
*Are investors Reluctant to Realize their Losses?***The Journal of Finance 53(5).**1775-1798.

Stock Options as Lotteries - by Utah Professors Brian H. Boyer and Keith Vorkink

14:53

Bonus Lecture: My Special Udemy Coupon Offer to You

Bonus Lecture: My Special Udemy Coupon Offer to You

00:11

About the Instructor