18.642 | Fall 2024 | Undergraduate

Topics in Mathematics with Applications in Finance

Week 12

Lecture 21

Video description: This lecture explores the fundamental concept of risk-neutral pricing as a powerful framework for derivative valuation, illustrated through examples like forward contracts and options. It further explains the derivation of the Black-Scholes equation from stochastic calculus, highlighting how derivative prices depend primarily on volatility and interest rates, not on investors’ risk preferences, and concludes with practical insights into option replication and hedging strategies.

Risk Neutral Valuation, Black-Scholes Equation Slides (PDF)

Lecture 22

Guest lecture with Ross Garon, Millennium Management

Lecture 22: The Spectrum of Systematic Trading Strategies in Liquid Instruments    
Note: This lecture is not available to OCW learners.

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