# 2022/23 Taught Postgraduate Module Catalogue

## MATH5350M Computations in Finance

### 15 creditsClass Size: 70

Module manager: Dr Jon Ward
Email: J.A.Ward@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2022/23

### Pre-requisite qualifications

Intermediate knowledge of programming in Python, e.g. MATH5306M Introduction to Programming or similar. Implementations of numerical algorithms will be required in assessed coursework. No training in programming will be provided.

### Co-requisites

 MATH5330M Continuous Time Finance

This module is not approved as an Elective

### Objectives

The aim of this module is to introduce the standard computational methods in financial mathematics and their application to securities pricing. There is a strong emphasis on practical implementation and numerical simulation.

On completion of this module, students will be able to:
- explain the basic modelling tools for financial options;
- generate random numbers with specified distributions;
- numerically solve stochastic differential equations;
- carry out Monte Carlo simulations to price financial derivatives;
- explain techniques for improving simulation accuracy and efficiency;
- demonstrate an understanding of numerical methods for PDEs;
- use finite difference methods to price European and American options;
- estimate price sensitivities (the Greeks).

### Syllabus

Pricing financial instruments and valuing new securities requires advanced numerical methods. Financial analysts routinely apply computational techniques to assess risk, price exotic options or value interest rate derivatives. A good command of the essential computational tools used in the financial service industry is expected from quantitative analysts.

This module covers Monte Carlo simulations and finite difference methods for financial derivative pricing. These two methods (both are standard workhorses) are essential in analysing securities that are modelled by stochastic or partial differential equations. Practical skills are emphasised and students will learn how to implement (and improve accuracy and efficiency of) numerical methods for financial valuation.

On completion of this module the student will be familiar with numerical methods in financial mathematics and will be able to apply and implement these methods to price financial derivatives.

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 11 2.00 22.00 Practical 3 1.00 3.00 Seminar 11 1.00 11.00 Private study hours 114.00 Total Contact hours 36.00 Total hours (100hr per 10 credits) 150.00

### Private study

2- 5 hours per lecture: 55 hours
- 5 hours per class: 55 hours
- Preparation for assessment: 20 hours

### Opportunities for Formative Feedback

Exercises will be handed in for assessment on a bi-weekly basis.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment . 40.00 Total percentage (Assessment Coursework) 40.00

The resit for this module will be 100% by examination

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 00 mins 60.00 Total percentage (Assessment Exams) 60.00

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