# 2007/08 Taught Postgraduate Module Catalogue

## MATH5330M Continuous Time Finance

### 15 creditsClass Size: 100

Module manager: Klaus Reiner Schenk-Hoppé
Email: K.R.Schenk-Hoppe@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2007/08

This module is not approved as an Elective

### Objectives

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.

### Syllabus

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

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 Lecture 10 2.00 20.00 Tutorial 10 1.00 10.00 Private study hours 120.00 Total Contact hours 30.00 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

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

Exams
 Exam type Exam 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