Stochastic Processes and Financial Applications

• Credit value: 15 credits at Level 7
• Convenor: Anthony Brooms
• Prerequisites: Probability and Stochastic Modelling and Statistical Analysis
• Assessment: coursework assignment(s) (20%) and a one-hour 40-minute (plus 15 minutes' reading time) examination (80%)

This module explains the theory of continuous time stochastic processes and stochastic differential calculus and how they are applied to solve problems in mathematical finance, in particular contingent claim pricing by martingale methods.

Indicative module syllabus

• Options: basic examples and simple arbitrage relationships
• The binomial model
• Hedging and the Black and Scholes equation
• Solving the Black and Scholes equation and deriving the Black and Scholes formula
• The Greeks of an option, their interpretation and their computation
• Path dependent options
• Monte Carlo pricing

By the end of this module, you should be able to:

• understand how to price financial assets using martingale methods
• understand the role and importance of absence of arbitrage in setting up the models
• know the difference between complete and incomplete market models, and the implications for pricing
• set up mathematical models for financial asset prices satisfying the principle of no-arbitrage, and how to compute these prices in such models.