Course co-ordinator(s): Dr Mateusz Majka (Edinburgh), Dr Adrian Nathai (Malaysia).
Aims:
This course develops the theory and practice of financial derivatives pricing in continuous time. The course contributes towards exemption from the CT8 examination of the Faculty and Institute of Actuaries
Summary:
We shall introduce the Black Scholes model, and look at some simple extensions to treat dividends/currencies.
We will look at bond pricing and the term structure of interest rates in an arbitrage-free framework. We will also cover how to price bond derivatives, and look at models of credit risk.
This course will concentrate on the application of stochastic modelling, however it will also require some of the basics of the theory of stochastic process, in particular a knowledge of Brownian motion and its properties.
Detailed Information
Course Description: Link to Official Course Descriptor.
Pre-requisite course(s): F79SP Stochastic Processes & F79DF Derivative Markets and Discrete-time Finance .
Location: Edinburgh.
Semester: 1.
Syllabus:
- Theory of Martingales in continuous time
- Brownian motion; definitions and properties
- Brownian motion as the limit of a binomial random-walk process
- Introduction to stochastic integration, stochastic differential equations and Ito's formula
- Geometric Brownian motion; the Ornstein-Uhlenbeck process
- Introduction to Girsanov’s theorem and the martingale representation theorem
- The Black-Scholes model
- Derivatives pricing using the Black-Scholes model using the martingale and PDE approaches to pricing
- Extensions to foreign currencies and dividend-paying stocks
- Portfolio risk management using the Greeks
- Introduction to interest rate models
- Introduction to credit risk models
Reading list:
The following books are recommended:
- Hull, J., (2000) Options, futures and other derivative securities, 4th ed, Prentice Hall;
- Baxter, M. and Rennie, A. (1996), Financial calculus, Cambridge University Press;
Students may also find the following books useful:
- Luenberger, D.G. (1998) Investment science. Oxford University Press.
- Bingham, N. H. & Kiesel, R. (1998) Risk neutral valuation. Pricing and hedging of financial derivatives. Springer Verlag;
- Björk, T. (1998) Arbitrage theory in continuous time. Oxford University Press;
SCQF Level: 10.
Credits: 15.
Other Information
Help: If you have any problems or questions regarding the course, you are encouraged to contact the course leader.
Canvas: further information and course materials are available on Canvas