Introductory description

This module runs in Term 1 and is available only to students in the Department of Statistics.

Pre-requisites: ST318 Probability Theory and ST339 Introduction to Mathematical Finance.

Leads To: ST909 Continuous Time Finance for Interest Rate Models.

Results from this module may be partly used to determine exemption eligibility in the Institute and Faculty of Actuaries module CM2. (Independent application with the IFoA may be required to receive the exemption.)

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Content:
Introduction to Brownian Motion and Stochastic Calculus.
Introduction to SDEs (Stochastic Differential Equations) and Markov processes.
Continuous-time models of security prices.
Risk-neutral evaluation and equivalent martingale measures, Girsanov and martingale representation theorems.
Black-Scholes theory: PDE and SDE approaches.
Basic Greeks, delta-hedging.
Put-Call parity and Put-Call symmetry.
Introduction to optimal stopping and American Options.
Bond prices and term structure of interest rates: Hull-White, Vasicek and CIR models.

Learning outcomes

By the end of the module, students should be able to:

• Know how probability models are used in financial mathematics
• Understand the concept of Brownian motion

Indicative reading list

View reading list on Talis Aspire

Subject specific skills

• Demonstrate facility with rigorous stochasticmethods.

• Evaluate, select and apply appropriate mathematical and/or probabilist techniques.

• Demonstrate knowledge of and facility with formal probability concepts, both explicitly and by applying them to the solution of finance problems.

• Create structured and coherent arguments communicating them in written form. 

• Construct logical mathematical arguments with clear identification of assumptions and conclusions.

• Reason critically, carefully, and logically and derive (prove) mathematical results.

Transferable skills

Problem solving: Use rational and logical reasoning to deduce appropriate and well-reasoned conclusions. Retain an open mind, optimistic of finding solutions, thinking laterally and creatively to look beyond the obvious. Know how to learn from failure.

• Self awareness: Reflect on learning, seeking feedback on and evaluating personal practices, strengths and opportunities for personal growth.

• Communication: Present arguments, knowledge and ideas, in a range of formats.

• Professionalism: Prepared to operate autonomously. Aware of how to be efficient and resilient. Manage priorities and time. Self-motivated, setting and achieving goals, prioritising tasks.