Prof Pauline Barrieu

This course is available on the BSc in Financial Mathematics and Statistics. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.

MA203 Real Analysis. Must be taken with ST202 Probability, Distribution Theory and Inference.

This course introduces the concepts of valuation, hedging and portfolio selection in a discrete-time environment with full technicalities, and then treats continuous-time markets in a slightly more heuristic fashion. It covers the following topics:

• Martingale theory in discrete time.

• The binomial model; pricing and hedging. Trinomial model and incompleteness, arbitrage-free price intervals.

• General discrete-time models and the FTAP.

• Passage to continuous-time Black & Scholes model; formal Ito calculus.

• Option-pricing with PDE methods, the Black & Scholes formula and Greeks; connections with risk-neutral measure, Feynman-Kac

• Portfolio optimisation (Merton's problem) in the standard Black & Scholes market

20 hours of lectures and 10 hours of seminars in the LT.

Students will be expected to produce 9 problem sets in the LT.

Lecture notes will be provided.

Stochastic Calculus for Finance I: The Binomial Asset Pricing Model, by Steven Shreve, Springer

Exam (100%, duration: 2 hours, reading time: 15 minutes) in the main exam period.