Section: Intercollegiate Classes | B8.3 Mathematical Models of Financial Derivatives (2025-26)

Lecturer: Profile: Sam Howison

Course information

General prerequisites:

B8.1 Probability, Measure and Martingales (previously named Martingales Through Measure Theory) would be good background. Part A Probability is a prerequisite. Part A Integration is also good background, though not a prerequisite.

Course term: Hilary

Course lecture information: 16 lectures

Course weight: 1

Course level: H

Assessment type: Written Examination

Course overview:

The course aims to introduce students to derivative security valuation in financial markets. At the end of the course the student should be able to formulate a model for an asset price and then determine the prices of a range of derivatives based on the underlying asset using arbitrage free pricing ideas.

Learning outcomes:

Students will have a familiarity with the mathematics behind the models and analytical tools used in Mathematical Finance. This includes being able to formulate a model for an asset price and then determining the prices of a range of derivatives based on the underlying asset using arbitrage free pricing ideas.

Course synopsis:

Overview of asset types, financial markets (including Limit Order Books) and derivative contracts
Discounting, arbitrage, and other basic financial arguments
Discrete-time models (binomial trees)
Introduction to Brownian motion and stochastic calculus; Ito's Lemma; conditional expectations and the Feynman-Kac formula
Hedging in continuous times and the Black-Scholes model
European-style option valuation: the Black-Scholes formulae as discounted expectations and as solutions of the Black-Scholes PDE. More general payoffs
American-style options
Mistage, barrier and other exotic options
Hedging and the Greeks: implied volatility. Extensions to the Black-Scholes model

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Section outline