This project focuses on different methods for pricing option, focused on European and American options.
💡 Click on links to find relevant code and/or theory for respective pricing method
European options are options that gives the buyer right, but not the obligation to buy (call option) or sell (put option) an underlying asset at a specific price (strike price) on a specific date (expiration date). Both Binomial Model and Black-Scholes are implemented here to calculate price of European options.
American options are options that gives the buyer right, but not the obligation to buy (call option) or sell (put option) an underlying asset at a specific price (strike price) on or before a specific date (expiration date). Longstaff Schwartz is implemented here to calculate price of American options.
In this notebook a few of the most popular option trading strategies are implemented (Long Straddle, Covered Call, Bear Put Spread, Long Call Butterfly Spead) showing their respective payoff-functions.
Bear Put Spread (left) and Covered Call (right)
Long Straddle (left) and Long Call Butterfly (right)
In this notebook, some important concepts in option pricing are shown such as convergence of option price in binomial model to Black-Scholes, put-call parity, price of american options compared to european.
Convergence of Binomial Model price to Black-Scholes price with increasing no. of steps
With smaller timte steps, the option price using binomial model will convergence to the price from Black-Scholes.
Example of GBM (Geometric Brownian Motion) outcomes
By simulating future possible stock movements (using GBM), Longstaff-Schwartz can calculate optimal exercise timing. Since American options can also be exercised before maturity, the expected value and probability of being in-the-money is higher for American options and hence their price is higher.
Price of American Option compared to European
The gap in price increases with time to maturity since this gives American options more time to be exercised in-the-money. Even at shorter maturity and options out-of-money, it holds that American options always are as expensive or more expensive than their European counterparts.