MATH5320M Discrete Time Finance

15 creditsClass Size: 120

Module manager: Dr Georgios Aivaliotis
Email: g.aivaliotis@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2021/22

Pre-requisite qualifications

The qualifications to gain entrance to the MSc in Financial Mathematics are sufficient.

This module is mutually exclusive with

 MATH3733 Stochastic Financial Modelling

This module is not approved as an Elective

Objectives

The aim of this module is to develop a general methodology for the pricing of financial assets in risky financial markets based on discrete-time models.

On completion of this module, students will be able to:
- describe the main instruments available in financial markets;
- apply the concepts of no-arbitrage and mean-variance to calculate fair prices of assets in one-period models;
- value risky returns with the Capital Asset Pricing Model and apply the Arbitrage Pricing Theory;
- demonstrate an understanding of the no-arbitrage principle in multi-period models;
- describe the Cox-Ross-Rubinstein binominal model and its applications;
- understand simple interest rate models;
- explain the fundamental differences between finite and infinite investment horizons;
- demonstrate an understanding of log-optimum investment and the Kelly rule.

Syllabus

Financial investments such as stocks, options and futures are risky: their prices can go down as well as up. This module will develop the necessary mathematical tools and models of financial markets to enable investors to value such assets. After completing the module, the student will know how to calculate the right discount rate to compensate for the risk of a financial instrument.

The focus is on models of efficient markets in discrete time. Standard models such as the Captial Asset Pricing Model (CAPM), the Arbitrage Pricing Theory, and Cox-Ross-Rubinstein as well as simple interest rate models are covered. Investments with an infinite time horizon - which are quite different to finite-horizon models - are discussed in connection with log-optimal investment and the Kelly rule.

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

Teaching methods

 Delivery type Number Length hours Student hours Lecture 11 1.00 11.00 Seminar 11 1.00 11.00 Private study hours 128.00 Total Contact hours 22.00 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

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 00 mins 100.00 Total percentage (Assessment Exams) 100.00

The resit for this module will be 100% by 2 hours examination