## MA320-7-SP-CO:Financial Derivatives

The details
2024/25
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Spring
Current
Monday 13 January 2025
Friday 21 March 2025
15
16 May 2024

Requisites for this module
(none)
(none)
(none)
(none)

(none)

## 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 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 the basic properties of Brownian motion, Ito's integral and the role of stochastic differential equations in finance.

2. Communicate and illustrate the importance of arbitrage arguments in modern finance.

3. Use a binomial model to evaluate derivatives.

4. An appreciation of the significance and limitations of the Black-Scholes-Merton model. This includes the construction and application of the Greeks in hedging.

5. Understand the main models for interest rates.

6. Demonstrate knowledge of simple credit rate models.

## Module information

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

Indicative syllabus

Brownian motion: properties. 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.
Interest rate derivatives: term structure, one-factor diffusion models, Vasicek and other common models.
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.

## Bibliography*

This module does not appear to have a published bibliography for this year.

## 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.

Coursework Exam
30% 70%

### Reassessment

Coursework Exam
30% 70%
Module supervisor and teaching staff
Dr John O'Hara, email: johara@essex.ac.uk.
Dr John O'Hara
maths@essex.ac.uk

Availability
No
No
No

## External examiner

Dr Melania Nica
Resources
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

* Please note: due to differing publication schedules, items marked with an asterisk (*) base their information upon the previous academic year.

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