- Department: Mathematics
- Module co-ordinator: Dr. Andrea Meireles Rodrigues
- Credit value: 20 credits
- Credit level: H
- Academic year of delivery: 2021-22
- See module specification for other years: 2022-23
Pre-requisite modules
Co-requisite modules
- None
Prohibited combinations
- None
This module is only available to students on the BSc in Actuarial Sciences.
Occurrence | Teaching period |
---|---|
A | Spring Term 2021-22 |
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.
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.
[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]
Task | Length | % of module mark |
---|---|---|
Essay/coursework Mathematical Finance for Actuarial Science Project |
N/A | 25 |
Online Exam -less than 24hrs (Centrally scheduled) Mathematical Finance for Actuarial Science |
3 hours | 75 |
None
Task | Length | % of module mark |
---|---|---|
Essay/coursework Mathematical Finance for Actuarial Science Project |
N/A | 25 |
Online Exam -less than 24hrs (Centrally scheduled) Mathematical Finance for Actuarial Science |
3 hours | 75 |
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.