B8.3 Mathematical Models of Financial Derivatives (2026-27)
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- 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 and ASO Integral Transforms are 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
- Multistage, barrier and other exotic options
- Hedging and the Greeks: implied volatility. Extensions to the Black-Scholes model
Section outline
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The dark-mode slides as used in lectures. NOT SUITABLE FOR PRINTING. And the same in normal light-mode. Take your pick.
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Slides from 23/24 (as the course was given by Alvaro Cartea, they take a slightly different approach in places; hence only for background/alternative perspectives).
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Lecture notes from 2023/24 by Alvaro Cartea. They are close to the course but may take a different approach in places.
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The website shows a lot of option prices: have a look around to familiarise yourself with them.
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Live evolution of the Bitcoin price as seen in Lecture 1. Note the order book and trade list feeds.
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Registration start: Monday, 11 January 2027, 12:00 PMRegistration end: Friday, 12 February 2027, 12:00 PM
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Class Tutor's Comments Assignment
Class tutors will use this activity to provide overall feedback to students at the end of the course.
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