Black Scholes Model

Build the core mathematical machinery — limits, derivatives, integrals, and series expansions — needed to manipulate the functions and equations that underpin the Black-Scholes PDE.

Establish the language of randomness — probability spaces, random variables, expectations, and key distributions — so you can formally describe the uncertainty in asset prices.

Understand the summary measures used to characterise return distributions and calibrate model parameters from observed market data.

Learn the financial building blocks — time value of money and option contracts — that define what the Black-Scholes model is actually pricing.

Tie everything together: market efficiency assumptions, discrete-to-continuous pricing via binomial trees, risk-neutral valuation through martingales and change of measure, and finally the derivation of the Black-Scholes formula itself.