Black-Scholes Formula and Risk Neutral Valuation - Lecture 21

Explore the fundamental concept of risk-neutral pricing as a powerful framework for derivative valuation in this 80-minute mathematics lecture from MIT's Topics in Mathematics with Applications in Finance course. Examine how risk-neutral valuation works through practical examples including forward contracts and options, understanding why derivative prices depend primarily on volatility and interest rates rather than investors' risk preferences. Learn the derivation of the Black-Scholes equation from stochastic calculus principles, discovering how this groundbreaking formula revolutionized options pricing. Gain practical insights into option replication strategies and hedging techniques that form the foundation of modern quantitative finance. Master the mathematical framework that enables traders and risk managers to price complex derivatives and construct hedging portfolios, with detailed explanations of the underlying stochastic processes and partial differential equations that govern option pricing models.