SVI 301 · Tier 300 — Advanced — Stochastic & Volatility · 3 credits

Stochastic Calculus & Black–Scholes

Brownian motion, Itô calculus, risk-neutral pricing, Black–Scholes, and the Greeks the platform shows on every option.

Prerequisites

Explain the leap from discrete-time series to continuous-time stochastic calculus, and why options pricing requires it.
Construct a scaled random walk and take its continuous-time limit to recover standard Brownian motion.
State the Itô multiplication table and write a stochastic differential equation, reading off its drift and diffusion.
State the no-arbitrage principle, the law of one price, and replication as the engine of derivative pricing.
State the Black–Scholes–Merton formula for a European call and put and identify what each input controls.
State and interpret the four primary Greeks — delta, gamma, vega, and theta — as partial derivatives of the Black–Scholes price.
Define rho, vanna, charm, and volga as second-order partial derivatives of the option price, and state what each one measures.