Financial Derivatives

The details
Mathematical Sciences
Colchester Campus
Postgraduate: Level 7
Monday 13 January 2020
Friday 20 March 2020
01 October 2019


Requisites for this module



Key module for

DIP GN1309 Mathematics and Finance,
MSC GN1312 Mathematics and Finance,
MSC GN1324 Mathematics and Finance,
DIP N32309 Actuarial Science,
MSC N32312 Actuarial Science

Module description

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.

Module aims

The aim of the module is tto gain insight into the methods used for pricing various financial derivatives and risk management.

Module 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.

Module information

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.

Learning and teaching methods

Contact hours: 43 hours Lectures: 35 sessions Problem classes: 5 sessions Summer revision: 3 hours


This module does not appear to have a published bibliography.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Weighting
Written Exam Test 1
Written Exam Test 2
Exam 120 minutes during Summer (Main Period) (Main)

Overall assessment

Coursework Exam
20% 80%


Coursework Exam
0% 100%
Module supervisor and teaching staff
Dr John O'Hara, email
Dr John O'Hara (



External examiner

Dr Dimitrina Dimitrova
Cass Business School, City, University of London
Senior Lecturer
Available via Moodle
Of 47 hours, 41 (87.2%) hours available to students:
6 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).


Further information
Mathematical Sciences

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