Mathematical Finance
| Code | School | Level | Credits | Semesters |
| MATH3015 | Mathematical Sciences | 3 | 20 | Spring UK |
- Code
- MATH3015
- School
- Mathematical Sciences
- Level
- 3
- Credits
- 20
- Semesters
- Spring UK
Summary
In this module the concepts of discrete time Markov chains studied in the module MATH2010 are extended and used to provide an introduction to probabilistic and stochastic modelling for investment strategies, and for the pricing of financial derivatives in risky markets. The probabilistic ideas that underlie the problems of portfolio selection, and of pricing, hedging and exercising options, are introduced. These include stochastic dynamic programming, risk-neutral measures and Brownian motion. The capital asset pricing model is described and two Nobel Prize winning theories are obtained: the Markowitz mean-variance efficient frontier for portfolio selection and the Black-Scholes formula for arbitrage-free prices of European type options on stocks. Students will gain experience of a topic of considerable contemporary importance, both in research and in applications.
Target Students
Available to single and joint honours mathematics students, including Statistics and Mathematical Finance.
Classes
- One 2-hour lecture each week for 10 weeks
- Two 1-hour lectures each week for 10 weeks
Assessment
- 100% Exam 1 (3-hour): Written examination
Assessed by end of spring semester
Educational Aims
The purpose of this module is to broaden the students' knowledge and experience of stochastic processes by studying their application in the important area of financial modelling.This module is in the Probability Pathway and builds upon the concepts of stochastic processes introduced in the module MATH2010. Students will acquire knowledge and skills relevant to the mathematical modelling of investment and finance.Learning Outcomes
A student who completes this module successfully should be able to:
L1 - formulate the capital asset pricing model;
L2 - apply stochastic dynamic programming techniques to solve financial asset decision-making problems;
L3 - state and apply concepts of arbitrage, hedging and option pricing in one-period asset models;
L4 - state and apply the multi-period Binomial options pricing model (Cox-Rubinstein), including the use of a risk-neutral/arbitrage measure;
L5 - derive and apply the Black-Scholes formula.