This module introduces the basic mathematical techniques underlying the modelling of derivative pricing.

A student will acquire skills on the development and application of pricing and risk management.
An introduction to stochastic methods is presented. Emphasis is placed risk-neutral valuation, the Black-Scholes-Merton model and interest rate models. The module also includes a brief introduction to credit risk.


To gain insight into the methods used for pricing various financial derivatives and risk management.

Learning Outcomes

By the end of this module a student should:

1. Understand and applying the properties of Brownian motion, Ito's integral and the role of stochastic differential equations in finance.
2. Apply arbitrage arguments in modern finance.
3. Use discrete methods to evaluate derivatives, and illustrate the EMM method.
4. An appreciation of the limitations of the Black-Scholes-Merton model and how these deficiencies can be mitigated. This includes the construction and application of the Greeks in hedging.
5. Understand and apply the stochastic models for interest rates.
6. Demonstrate knowledge of simple credit rate models.


Brownian motion: properties and applications. Ito's integral, Ito's lemma, stochastic differential equation.

Pricing derivatives: arbitrage arguments, complete market, forward contracts, binomial methods, risk-neutral pricing, state-price deflator, Black-Scholes-Merton model, martingales, Garman-Kohlhagen, hedging. Applications.

Interest rate derivatives: term structure, one-factor diffusion models, Vasicek and other common models. Yield curve.

Credit risk: credit event, modelling credit risk, Merton model, two state model.