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# Mathematical Finance for Actuarial Science - MAT00059H

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• Department: Mathematics
• Module co-ordinator: Dr. Andrea Meireles Rodrigues
• Credit value: 20 credits
• Credit level: H
• Academic year of delivery: 2019-20

## Module will run

Occurrence Teaching cycle
A Spring Term 2019-20

## Module aims

• The martingale approach to asset pricing.

• The Black-Scholes PDE

• Black-Scholes formula for option pricing in continuous time.

• Merton model of credit risk.

• To introduce stochastic term structure models as applied to pricing interest rate derivatives;

• To introduce a range of models for credit risk and credit ratings.

## Module learning outcomes

At the end of the module the student should be able to understand and apply:

• the martingale approach to asset pricing

• the Black-Scholes PDE and formula for option pricing

• different approaches to modelling credit risk and credit ratings

• some models of the term structure of interest rates and apply them to price basic interest rate derivatives.

## Module content

[This module is only available to students on BSc Actuarial Science.]

• American options as a discrete time model

• Revision of Stochastic Calculus

• Girsanov’s Theorem.

• The Black-Scholes model for a stock market.

• The Black-Scholes partial differential equation.

• The Black-Scholes pricing formula for European call options.

• The risk neutral measure and pricing in the Black-Scholes model.

• The Greek parameters.

• The Merton model as an example of a structural model of credit risk

• Further examples of stochastic differential equations and the Ornstein Uhlenbeck process

• modelling credit risk: reduced form models and intensity based models.

• The two-state model for credit ratings and the Jarrow-Lando-Turnbull model

• Models of the term structure of interest rates, including one-factor general diffusion model, and the Vasicek, Cox-Ingersooll-Ross and Hull-White models

• Pricing some standard interest rate derivatives in the above models

## Assessment

Task Length % of module mark
Online Exam
Mathematical Finance for Actuarial Science
N/A 100

None

### Reassessment

Task Length % of module mark
Online Exam
Mathematical Finance for Actuarial Science
N/A 100

## Module feedback

Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

• G R Grimmett & D R Stirzaker, Probability and random processes, OUP.

• C W Gardiner, Handbook of stochastic methods, Springer.

• M Capinski and T Zastawniak, Mathematics for Finance; An Introduction to Financial Engineering, Springer.

• T Mikosch, Elementary stochastic calculus with finance in view, World Scientific.

• Z Brzezniak & T Zastawniak, Basic Stochastic Processes, Springer.

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.