Financial Derivatives

The details
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Postgraduate: Level 7
Monday 13 January 2025
Friday 21 March 2025
18 March 2024


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,
MSC N32324 Actuarial Science,
MPHDN32348 Actuarial Science,
PHD N32348 Actuarial Science

Module description

This module introduces the basic mathematical techniques underlying the modelling of derivative pricing. Students 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 aims of this module are:

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

  • to use finance theories, discrete-time and continuous-time models to price and hedge the most important options, futures and other derivatives.

Module learning outcomes

By the end of the module, students will be expected to:

  1. Understand and apply 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. Have 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. Value basic benefit guarantees using option pricing techniques

  6. Understand and apply the stochastic models for interest rates.

  7. Demonstrate knowledge of simple credit rate models.

  8. Implement financial derivatives models in Microsoft Excel spreadsheet, using some of Excel's built-in financial and statistical functions and other useful tools.

Module information

This module covers part of the Institute and Faculty of Actuaries CM2 syllabus.

Indicative syllabus

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

Teaching in the School will be delivered using a range of face to face lectures, classes and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.


The above list is indicative of the essential reading for the course.
The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students.
Further reading can be obtained from this module's reading list.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Coursework weighting
Coursework   Test     
Exam  Main exam: In-Person, Open Book (Restricted), 120 minutes during Summer (Main Period) 
Exam  Reassessment Main exam: In-Person, Open Book (Restricted), 120 minutes during September (Reassessment Period) 

Exam format definitions

  • Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
  • In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
  • In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
  • In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary, for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.

Your department will provide further guidance before your exams.

Overall assessment

Coursework Exam
30% 70%


Coursework Exam
30% 70%
Module supervisor and teaching staff
Dr John O'Hara, email:
Dr John O'Hara



External examiner

Dr Melania Nica
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

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