MSc in Mathematical Finance

by Online Distance Learning

make options your future

make futures your option

**MODULE SPECIFICATIONS**

**Mathematical Finance Dissertation (Online Version)**

Level M, Dissertation Stage, 60 credits

Code: MAT00026M

**Pre-requisites:** Completing the Certificate and Diploma Stages of the MSc in Mathematical Finance

**Aims and Distinctive Features:** Candidates for the MSc degree will submit a dissertation of around 60 pages on a selected topic in Mathematical Finance. Support and advice will be provided by individual dissertation supervisors and consultants.

Students submitting a dissertation will be expected to demonstrate the ability to absorb and analyse current research literature in mathematical finance and/or to apply their skills of implementation of mathematical models in concrete situations arising in financial engineering practice. Original contribution to research, while laudable, will not be required.

**Learning Outcomes:** By the end of this module students should

a) demonstrate an ability for in-depth independent research into a chosen topic in mathematical finance;

b) provide evidence in their dissertation of their ability to read and understand current research literature in this field;

c) where appropriate for the selected topic, develop and apply computer software to present a solution to the problem at hand;

d) present the outcome of their research and the background for the chosen topic in a self-consistent, clear, rigorous and accessible manner;

e) demonstrate the ability to locate and understand current literature in the selected area of their research;

f) present a critical approach emphasizing the strengths and limitations of the approaches, methods, and solutions studied.

**Indicative Content:** The choice of dissertation/project topics from a list provided by the department will be made by each student after consultation with the supervisor. Possible dissertation topics include but are not limited to the following:

Risk-Free and Risky Asset Models (term structure and advanced interest rate models, for example, Vasicek model, Hull-White model, Cox-Ingersoll-Ross model, Heath-Jarrow-Morton model, Markov chain model , portfolios of bonds an immunisation techniques, advanced mathematical models of stock prices);

Risk and Portfolio Management (market efficiency, efficient frontier, constrained portfolios)

Derivative Financial Instruments (Forwards and Futures, European and American options, valuation and replication strategies, Cox-Ross-Rubinstein and Black-Scholes pricing formulae and their generalisations (transaction costs, incomplete markets, markets with friction), exotic options, 2nd generation options, exchanges rate and index options, application of control theory in option pricing, numerical methods)

Optimisation Techniques (maximisation of utility, cost minimising, models involving consumption, linear programming, the simplex method, non-linear programming, Kuhn-Tucker theorem, application to option pricing in incomplete markets).

Examples of possible dissertation/project topics used previously for the campus-based MSc in Mathematical Finance:

Construction of martingale measures by maximizing entropy

Continuous time limit of the binomial model

Estimating volatility using ARCH models

Optimal investments using utility functions

Real options

Mean-VaR portfolio theory

Liquidity risk by means of VaR

Valuation of companies

Coherent risk measures

Capital structure

Optimal portfolios in Heath-Jarrow-Morton model

Conditional Value at Risk

Applications of change of numeraire for option pricing

Copulas in finance

Single factor short rate models

Modelling credit risk - structural approach

Credit risk - reduced form approach

Credit risk - probabilities of default

Computer simulations of interest rate models

Stochastic differential delay equations in finance

Methods of designing pension schemes

Fundamental theorem of asset pricing and its extensions

Implied volatility, volatility smile, stochastic volatility

Complete market models implied by call options

Monte Carlo valuation of American type derivative securities

Microscopic simulation of the stock market

Pricing weather derivatives by utility maximisation

Arbitrage pricing of mortgage-backed securities

Computer implementation of finite-difference option pricing schemes

**Learning and Teaching Strategy:**

- Students will select a topic from a list provided, but will also be encouraged to design their own topic subject to approval by the potential supervisor.

- Supervisory backup will be provided individually to each student on a regular basis by means of online sessions with the dissertation supervisor. Typically 6 one-hour sessions will be scheduled at regular intervals during the Dissertation Stage.

- Students are expected to submit their written work electronically on a regular basis prior to their scheduled supervisory sessions, which will read be returned with comments by the supervisor or consultants.

- Students will be required to pass an online viva at the end of the Dissertation Stage.

- E-mail support will be provided by the supervisor and consultant.

- Further support to be provided through the VLE platform, proving file depository and other services.

**Arrangements for Revision and Private Study:** Students taking this module are expected devote approximately 600 hours of work to the dissertation. Progress will be monitored in regular online supervisory sessions and by requiring students to submit electronic drafts of their work in advance of supervisory meetings. Oral presentation during the online viva will provide students with a further opportunity to present their dissertation work in addition to the thesis submitted and to address any questions that may arise in connection with this work.

**Assessment:** The completed dissertation to be read and assessed independently by two internal referees who will produce a joint report, to be approved by the External examiner. A recorded online viva at the end of the Dissertation Stage will serve to authenticate the work submitted for assessment, but in normal circumstances will not affect the mark assigned for written work, unless there is evidence emerging during the viva that the student fails to have thorough understanding of the work submitted.

**Recommended Texts:** As per topic description