Stochastic Financial Modelling
| Code | School | Level | Credits | Semesters |
| MATH4018 | Mathematical Sciences | 4 | 20 | Spring UK |
- Code
- MATH4018
- School
- Mathematical Sciences
- Level
- 4
- Credits
- 20
- Semesters
- Spring UK
Summary
In this course the concepts of discrete time Markov chains studied in MATH4019 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 and hedging options, are introduced. These include 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. A project will be undertaken which will involve independent reading, and a written report.
Target Students
Students taking MSc in Statistics, MSc in Statistics and Applied Probability, MSc Statistics with Machine Learning in the School of Mathematical Sciences. Not available to undergraduate students.
Classes
- Two 1-hour lectures each week for 10 weeks
- One 2-hour lecture each week for 10 weeks
Assessment
- 25% Coursework 1: 2,000 - 3,000 word essay
- 75% Exam 1 (3-hour): Written examination
Assessed by end of spring semester
Educational Aims
The purpose of this course is to broaden the students' knowledge and experience of stochastic processes by studying their application to the important area of financial modelling.This module builds upon the concepts of stochastic processes introduced in MATH4019. Students will acquire knowledge and skills relevant to the mathematical modelling of investment and finance. Also, research experience will be broadened by undertaking some independent but supervised reading, and summarising the material in a project report.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;
L6 - develop independent research and writing skills, through study of a research paper.