Mathematical Finance for Actuarial Science - MAT00059H

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Additional information

 

This module is only available to students on the BSc in Actuarial Sciences.

Module will run

Occurrence	Teaching period
A	Spring Term 2022-23

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

[This module shares the lectures, problems classes and seminars with Mathematical Finance II]

Indicative assessment

Task	% of module mark
Closed/in-person Exam (Centrally scheduled)	75.0
Essay/coursework	25.0

Special assessment rules

None

Indicative reassessment

Task	% of module mark
Closed/in-person Exam (Centrally scheduled)	75.0
Essay/coursework	25.0

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.

Indicative reading

• 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.