Quant finance Series of 3 42 min
Black-Scholes-Merton
What an option is, the Black–Scholes price of a call derived from scratch, and what happens to the formula when each assumption fails.
What you need Calculus, a little differential equations, and a first statistics course.
Start with Vol. I 2024
- I Options, Explained Calls and puts from both sides of the trade; European, American and Bermudan exercise; and the assumptions the Black-Scholes-Merton formula rests on.
- II Deriving BSM from Scratch Builds Brownian motion from coin flips, shows with Itô's lemma that a stock is lognormal, and integrates the call payoff to derive the Black-Scholes formula.
- III Nuance, and Other Approaches The Black-Scholes formula rederived from the heat equation and a change of numeraire, then each assumption relaxed: rates, dividends, the volatility smile.