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2008/09 Undergraduate Module Catalogue

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

MATH2750Introduction 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 typeNumberLength hoursStudent hours
Example Class71.007.00
Lecture261.0026.00
Practical31.003.00
Private study hours114.00
Total Contact hours36.00
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 typeNotes% 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 typeExam 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

Reading list

The reading list is available from the Library website

Last updated: 01/04/2009

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