Studying at York
Mathematical Finance for Actuarial Science - MAT00059H
Related modules
Pre-requisite modules
Co-requisite modules
- None
Prohibited combinations
- None
Additional information
This module is only available to students on the BSc in Actuarial Sciences.
Module will run
| Occurrence | Teaching cycle |
|---|---|
| A | Spring Term 2021-22 |
Module aims
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The martingale approach to asset pricing.
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The Black-Scholes PDE
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Black-Scholes formula for option pricing in continuous time.
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Merton model of credit risk.
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To introduce stochastic term structure models as applied to pricing interest rate derivatives;
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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:
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the martingale approach to asset pricing
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the Black-Scholes PDE and formula for option pricing
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different approaches to modelling credit risk and credit ratings
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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.]
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American options as a discrete time model
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Revision of Stochastic Calculus
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Girsanov’s Theorem.
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The Black-Scholes model for a stock market.
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The Black-Scholes partial differential equation.
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The Black-Scholes pricing formula for European call options.
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The risk neutral measure and pricing in the Black-Scholes model.
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The Greek parameters.
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The Merton model as an example of a structural model of credit risk
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Further examples of stochastic differential equations and the Ornstein Uhlenbeck process
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modelling credit risk: reduced form models and intensity based models.
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The two-state model for credit ratings and the Jarrow-Lando-Turnbull model
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Models of the term structure of interest rates, including one-factor general diffusion model, and the Vasicek, Cox-Ingersooll-Ross and Hull-White models
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Pricing some standard interest rate derivatives in the above models
[This module shares the lectures, problems classes and seminars with Mathematical Finance II]
Assessment
| Task | Length | % of module mark |
|---|---|---|
| Essay/coursework Mathematical Finance for Actuarial Science Project |
N/A | 25 |
| University - closed examination Mathematical Finance for Actuarial Science Exam |
3 hours | 75 |
Special assessment rules
None
Reassessment
| Task | Length | % of module mark |
|---|---|---|
| Essay/coursework Mathematical Finance for Actuarial Science Project |
N/A | 25 |
| University - closed examination Mathematical Finance for Actuarial Science Exam |
3 hours | 75 |
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
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G R Grimmett & D R Stirzaker, Probability and random processes, OUP.
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C W Gardiner, Handbook of stochastic methods, Springer.
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M Capinski and T Zastawniak, Mathematics for Finance; An Introduction to Financial Engineering, Springer.
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T Mikosch, Elementary stochastic calculus with finance in view, World Scientific.
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Z Brzezniak & T Zastawniak, Basic Stochastic Processes, Springer.
