## MATH3733 Stochastic Financial Modelling

### 15 creditsClass Size: 100

Module manager: Professor A. Yu Veretennikov
Email: veretenn@maths.leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2008/09

### Pre-requisites

 MATH2750 Introduction to Markov Processes

This module is approved as an Elective

### Module summary

Financial investments such as stocks and shares are risky: their value can go down as well as up. To compensate for the risk in a fair market, a discount is needed. This module will develop the necessary probabilistic tools to enable investors to value such assets.

### Objectives

To develop a general methodology based on stochastic analysis for the pricing of financial assets in risky financial markets.

By the end of this module, students should be able to:
a) describe the main instruments available in financial markets;
b) use filtrations and martingales to model any evolving state of knowledge in a fair market;
c) use appropriate stochastic methods to evaluate return rates on risky assets;
d) value options using the Black-Scholes theorem.

### Syllabus

Financial investments such as stocks and shares are risky: their value can go down as well as up. To compensate for the risk in a fair market, a discount is needed. This module will develop the necessary probabilistic tools to enable investors to value such assets.

Topics included:
1. Economic background. Markets, options, portfolios, hedging, arbitrage.
2. Discrete time stochastic processes. Conditional expectation, Markov chains, measure theory, filtrations, martingales, Doub-Meyer decomposition.
3. Discrete time finance. Asset pricing in a risky market, viability, discrete Black-Scholes formula, equivalent martingale measure.
4. Continuous time stochastic processes. Brownian motion, stochastic integrals, Ito calculus.
5. Continuous time finance. Geometric Brownian motion, asset prices, volatility, continuous Black-Scholes theorem.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

 Delivery type Number Length hours Student hours Example Class 7 1.00 7.00 Lecture 26 1.00 26.00 Practical 3 1.00 3.00 Private study hours 114.00 Total Contact hours 36.00 Total hours (100hr per 10 credits) 150.00

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Coursework
 Assessment type Notes % of formal assessment In-course Assessment . 20.00 Total percentage (Assessment Coursework) 20.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 3 hr 80.00 Total percentage (Assessment Exams) 80.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated