Analysis of the Delta-Gamma approximation formula and what it tells you about your option premium when considering its greeks and changing market conditions.

Real example on the platform applying the delta-gamma approximation formula to estimate a change in option premium as different conditions change (underlying price, volatility, time to expiration). This is carried out by considering first order greeks (Delta, Vega, Theta) plus also the effect of Gamma.

Factors that impact both intrinsic and extrinsic values on an option. Differences in the distribution of intrinsic and extrinsic values as stock prices go from out-of-the-money to at-the money to in-the-money.

Differences in the distribution of intrinsic and extrinsic values as stock prices go from out-of-the-money to at-the money to in-the-money as well as the impact of Implied Volatility and Time to Expiration.

Examples of the distribution of intrinsic and extrinsic values for different options on the thinkorswim platform.

Analysis and derivation of a quick formula to estimate the price of an ATM Straddle knowing a stock price, implied volatility and time to expiration. This is done by using the Black-Scholes-Merton model for European, non-dividend paying stocks in a zero percent risk-free interest rate environment as a good approximation for a quick and general formula for an ATM Straddle.

Use of the ATM Straddle as a measure of volatility that allows us to estimate delta for different options knowing how many multiples of the ATM straddle that option is away from the current stock price.

Estimating the price of an ATM straddle on the platform and what it tells us about a stock's options and their approximate delta.

Using what we learned about the ATM straddle and some basic greek calculations to quickly estimate the price of a 20-delta strangle knowing the ATM straddle price.

Estimating the value of a 20-delta strangle as an exercise with real data on the thinkorswim platform.

Introduction to what the Black-Scholes model is and how it is used to estimate the fair price of a European-style option.

Analysis and development of the Black-Scholes formula and how it's related to the price of an option. Discussion of all the assumptions that the Black-Scholes model makes with regards to the lognormal distribution of stock prices and how it can be modelled assuming geometric brownian motion.

Creation of your own option pricing spreadsheet by applying the Black-Scholes formulas in an excel file.

ATM Delta is normally approximated to 0.50 which is a very good approximation but not the real number. Application of Black-Scholes option pricing formulas to estimate an ATM delta number that is closer to reality and how implied volatility has an impact on it.

Probability of an option expiring ITM is normally approximated to its delta value which is a very good approximation but not the real number. Application of Black-Scholes option pricing formulas to estimate a real Probability of expiring ITM value that is related to, but not exactly delta.

What is Volatility Skew and howit affects option premiums. Which naked options and vertical spreads are cheap or expensive once IV skew is considered.

Strategies that incorporate IV skew into their setup to take advantage of it. In this lesson we analyze a Put Ratio Spread, a Jade Lizard and a Delta Buster.

Analysis of calendarized strategies such as calendar and diagonal spreads. Impact of greeks (delta, theta, gamma, vega) on both front and back legs.

Impact of an IV increase in the term structure of implied volatility. Analysis of a real example: SPX during the COVID crisis and how its IV explosion affected its term structure, focusing on the different reaction of front expirations vs back expirations and the impact it could have in calendarized positions.

How Vega needs to be adjusted to price in the effect of IV term structure in the price of calendarized options positions, so that you are aware of how those positions, which are nominally both long theta and long vega, can be misleading.

It's obvious that call buyers were big winners after the Gamestop short squeeze. In this lesson you will learn why put buyers were also winners, despite being completely wrong about price direction (hint: with options, it's all about Implied Volatility)

Analysis of the put-call parity formula and how it is a cornerstone of option pricing theory. Included in this lesson are the effect of dividends and the risk-free interest rate in put-call parity.

Creation of synthetic long and short stock positions applying put-call parity principles.

Application of put-call parity to known options strategies such as a covered call and a married put.

Real example: NKLA going through a short-squeeze and its impact on Hard-to-borrow status and short-selling fees.

Application of put-call parity in the pricing of options when considering high short-selling fees.

Impact of high short-selling fees in the pricing of options and potential early-exercise risk when selling calls on heavily-shorted underlyings.

How a box spread is structured and how it is constructed through the use of synthetic long and short stock positions.

Use of box spreads as borrowing or lending instruments. Impact of early-exercise on the pricing and risks of box spreads especially for retail traders.

Real examples of box spreads on the platform for both american and european-style options.

Analysis of a "free-money" box spread trade in the real market.

How early-exercise derailed a "free-money" box spread trade, highlighting the importance of analyzing all the risks related to a box spread trade before implementing it.

Analysis of the synthetic equivalence between a Covered Call and a short put, along with a review of their differences.

Real example analyzing the p/l risk profile of a covered call and its synthetic equivalent short put.

Application of put-call parity to confirm that Iron Condors and Butterflies are synthetically equivalent to Long Call and Put Condors and Butterflies.

Real examples on the platform comparing and contrasting Iron Condors and Butterflies to Long Call and Put Condors and Butterflies.

Application of put-call parity to confirm that Long Call Spreads and Long Put Spreads are synthetically equivalent to Short Put Spreads and Short Call Spreads respectively.

Visual representation of how the price of Vertical debit and credit spreads fluctuate and are related to each other as the underlying price changes.

Real examples on the platform comparing and contrasting Long Call and Put Spreads to Short Put and Call Spreads.

Review of 1st and higher order Option Greeks and what they measure and can tell us about options and options positions.

Review of Delta and how it changes as the underlying price, implied volatility and time to expiration change for different strike prices when analyzing a call option.

Review of Gamma and how it changes as the underlying price, implied volatility and time to expiration change for different strike prices  when analyzing a call or put option.

Review of Vega and how it changes as the underlying price, implied volatility and time to expiration change for different strike prices  when analyzing a call or put option.

Review of Theta and how it changes as the underlying price, implied volatility and time to expiration change for different strike prices  when analyzing a call or put option.

Summary of all first options Greeks (plus Gamma) and how they change as the underlying price, implied volatility and time to expiration change for different strike prices. Delta is applied to call options and all others greeks apply to both call or put options.

Differences between intrinsic and extrinsic values in the price of an option. Definition of premium and premium-selling options strategies.

Analyisis of premium-selling strategies by directional exposure for low to medium levels of Implied Volatility.

Analyisis of premium-selling strategies by directional exposure for high levels of Implied Volatility.

Vertical spreads are one of the most versatile and useful option strategies. They combine the exposure of stand-alone long or short calls or puts with the protection of pre-defined maximum losses and capital usage. In this lesson we take a look at Vertical spreads as we try to clarify the main reasons why option traders don't get the results they are hoping for when using either debit or credit spreads.

If you’re an options trader there’s a good chance that one your go-to strategies is a vertical spread. A vertical spread is made up of 2 legs, one that is bought and one that is sold; with the same number of contracts, in the same underlying, for the same expiration and of the same type call or put. The only difference between the 2 legs being their strike price. Today we’re going to look at some misconceptions about vertical spreads and how in reality you could say that call spreads can be put spreads and also that debit spreads can be credit spreads.

Impact of earnings releases in option prices. How Implied Volatility reacts to an upcoming earnings release.

How to calculate the expected stock price move due to a binary event such as an earnings release using options and what the option market is telling us about potential stock price action after the binary event.

How to implement a 1:1 50/50 options earnings play using an Iron Butterfly betting on the magnitude of the actual move being lower than the expected move.

How to implement a 1:1 50/50 options earnings play using an Iron Condor betting on the magnitude of the actual move being lower than the expected move.

How to calculate the potential losses on a 0 DTE SPX Iron Fly using the Black-Scholes-Merton option pricing model depending on SPX moves and when they happen during the course of the day.

Differences between Volatility, Implied Volatility and VIX. Analysis of what VIX represents and how it's calculated

Using VIX Futures to trade the VIX. Differences between contango and backwardation. Settlement process for VIX Futures

Using VIX ETFs and ETNs to trade the VIX. Differences between contango and backwardation and impact on pricing. Tracking accuracy analysis for VXX, UVXY and SVXY

Using VIX Options to trade the VIX. Analysis of ATM levels for VIX Options compared to spot VIX and VIX Futures. Guidelines for trading naked options and long calendarized positions on the VIX

Comparison between VIX Futures, VIX ETFs and ETNs and VIX Options.

Real-data analysis of SPX, VIX, VVIX and SPX Probability Cones using VIX on the Platform

Using VIX Futures, VIX ETFs and ETNs and VIX Options to trade VIX on the Platform

Additional Volatility Indices calculated by the CBOE: VIX, VXN, VXO, VXD, RVX, VIX9D, VIX3M, VIX6M, VIX1Y, VXEFA, VXEEM, VXFXI, VXEWZ, OVX, GVZ, VXSLV, VXGDX, VXXLE, EVZ, VXAZN, VXAPL, VXGS, VXGOG, VXIBM, VVIX

How to derive the value of VIX from SPX Options, which expirations to use and which products are the basis of most VIX ETPs

How to calculate the settlement value VRO for weekly expirations of VIX Futures and VIX Options

How to calculate the settlement value VRO for monthly expirations of VIX Futures and VIX Options

Which options' strikes are used when computing VIX and how do variance swaps come into play when calculating VIX

Differences between VRO (expiration cash-settlement value for VIX products) and VIX and analysis of their values over the last year