Section: Course Materials | B8.3 Mathematical Models of Financial Derivatives (2024-25)

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:

Discrete-time models (binomial trees) and arbitrage in finance
Hedging in continuous times and the Black-Scholes model
European-style options and
Introduction to Brownian motion and Ito's Lemma
American-style options, PDEs and the Feynman-Kac formula
Perpetual and other exotic options
Implied volatility: smiles and smirks
The Merton Jump-Diffusion model and option prices
Consumption-based pricing
Limit order books and optimal execution models

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