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2007/08 Taught Postgraduate Module Catalogue

MATH5330M Continuous Time Finance

15 creditsClass Size: 100

Module manager: Klaus Reiner Schenk-Hoppé

Taught: Semester 2 View Timetable

Year running 2007/08

This module is not approved as an Elective


This module develops a general methodology for the pricing of financial assets in risky financial markets based on continuous-time models. On completion of this module, students will be able to:

- demonstrate an understanding of continuous-time stochastic processes;
- interpret a stochastic differential equation and its solution;
- understand the log-normal asset pricing model;
- apply the Ito formula in simple examples;
- explain the Black-Scholes formula;
- understand the arbitrage principle and its application to securities pricing;
- derive the partial differential equation for arbitrage-free derivative securities prices;
- explain state prices and the concept of equivalent martingale measures;
- show an understanding of term-structure models.


Prices of financial securities are often adequately described by continuous-time stochastic processes derived from a Brownian motion. This module will cover the fundamental continuous-time models of financial markets and the necessary mathematical tools for their analysis. The students will learn to apply stochastic calculus and partial differential equations for pricing securities such as options, futures and interest rate derivatives in arbitrage-free markets.

This module is devoted to continuous-time stochastic processes, stochastic differential equations, the Ito formula, Black-Scholes formula, principle of arbitrage in continuous-time models, partial differential equations of securities prices, state prices, equivalent martingale measures and term-structure (interest rate) models.

On completion of this module the student will be familiar with the basic theory, tools and terminology of continuous-time financial mathematics and will be able to apply the models and techniques to analyse real world situations.

Teaching methods

Delivery typeNumberLength hoursStudent hours
Private study hours120.00
Total Contact hours30.00
Total hours (100hr per 10 credits)150.00

Private study

6 hours per lecture: 60 hours;
4 hours per tutorial: 40 hours;
Preparation for assessment: 20 hours.

Opportunities for Formative Feedback

Progress will be monitored by contributions made to tutorials; and there will be an informal test in about week 5.

Methods of assessment

Exam typeExam duration% of formal assessment
Standard exam (closed essays, MCQs etc)3 hr 100.00
Total percentage (Assessment Exams)100.00

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: 24/05/2010


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