- Lecturer: Sam Howison
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