Course Information Undergraduate prospectus

Advanced Finite Difference Methods for Derivatives Pricing (MMath)

Course summary

Course code: MATH1152
Level: 7
Credits: 15
School: Architecture, Computing and Hums
Department: Mathematical Sciences
Course Coordinator(s): Arthur Parrott

Specification

Pre and co requisites

Partial Differential Equations

Aims

To provide an introduction to the use of advanced finite difference methods.
To provide a detailed description of the use of finite difference methods for pricing early exercise, Asian options, options under stochastic volatility and options with jump diffusion.
To compare finite difference methods with Monte Carlo and integral methods for pricing exotic options.

Learning outcomes

On successful completion of this course a student will be able to:


1. Have an overall understanding of the stability, accuracy and consistency of advanced finite difference methods applied to PDEs.

2. Have a critical understanding of finite difference methods related to the solutions of option pricing problems.s.

3. Apply finite difference methods to early exercise, Asian, stochastic volatility and jump diffusion option, pricing option problems.

4. Have an appreciation and awareness of available tools for implementing finite difference methods for the solution of option pricing problems

Indicative content

Option pricing problems as PDEs; derivations of initial data and boundary conditions; single factor and two-factor option pricing PDEs; coordinate transformations and mesh placement; iteration techniques including Kylov subspace methods. Projection and penalty approaches to early exercise; Semi-Lagrange time integration. Matlab implementation.

Teaching and learning activity

Concepts and techniques will be introduced and demonstrated in lectures and laboratory sessions.

Assessment

Summative assessment: Coursework - 50%
LO - 1-4
Coursework covering all learning items, which may include selected tutorial exercises.

Summative assessment: Examination - 50%
LO - 1-4
Examination of 3 hours duration covering all learning outcomes.

Formative assessment: Weekly tutorial exercises