Course co-ordinator(s): Dr Wei Wei (Edinburgh).
Aims:
The aim of this model is to study the application of the Black-Scholes model to the range of derivative securities encountered in the market, and to the term structure of interest rates. The principle tool will be the equivalent martingale measure. Links between derivative prices and PDEs will be indicated but solution of PDEs will be covered elsewhere. Discrepancies between the Black-Scholes model and market data will be described, and alternative models presented.
Summary:
- The Black-Scholes PDE.
- Extension of the Black-Scholes model to stocks paying dividends, foreign exchange and derivatives on futures; futures prices under Q; market price of risk.
- Hedging and the Greeks; portfolio insurance.
- The term-structure of interest rates: spot rates, forward rates and the yield curve.
- Discrete-time interest-rate models.
- Continuous-time interest-rate models: Vasicek, Cox-Ingersoll-Ross, pricing interest rate derivatives; the Heath-Jarrow-Morton approach; other no-arbitrage models.
Detailed Information
Course Description: Link to Official Course Descriptor.
Pre-requisites: none.
Location: Edinburgh.
Semester: 2.
Learning Outcomes:
At the end of studying this course, students should be able to:
- Demonstrate how to price and hedge simple equity derivatives contracts.
- Show an awareness and understanding of the differences between the real-world and risk-neutral probability measures.
- Be able to apply the main models for the term-structure of interest rates for pricing bonds and interest-rate derivatives and prove the underlying theory.
Reading list:
HULL, J.C. (2000). Options, Futures and Other Derivatives (4th Edition). Prentice-Hall.
BAXTER, M. & RENNIE, A. (1996). Financial Calculus. CUP.
LAMBERTON, D. & LAPEYRE, B. (1996). Introduction to Stochastic Calculus Applied to Finance. Chapman & Hall.
BINGHAM, N.H. & KIESEL, R. (1998). Risk-Neutral Valuation. Pricing and Hedging of Financial Derivatives. Springer.
JAMES, J. & WEBBER, N. (2000). Interest-Rate Modelling. Wiley.
SCQF Level: 11.
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