Postgraduate Course: Derivative Pricing and Financial Modelling (MATH11057)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 11 (Postgraduate)
||Availability||Not available to visiting students
|Summary||The aim of this course 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.
This course is delivered by Heriot Watt University and is only available to students on the MSc Financial Mathematics programme.
The Black-Scholes PDE.
Extension of the Black-Scholes model to stocks paying dividends, foreign exchange and derivatives on futures; futures prices under the risk-neutral measure; 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.
Entry Requirements (not applicable to Visiting Students)
||Other requirements|| MSc Financial Mathematics students only.
Course Delivery Information
|Academic year 2017/18, Not available to visiting students (SS1)
|Learning and Teaching activities (Further Info)
Lecture Hours 40,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 3,
Directed Learning and Independent Learning Hours
|Additional Information (Learning and Teaching)
Examination takes place at Heriot-Watt University.
|Assessment (Further Info)
|Additional Information (Assessment)
||See 'Breakdown of Assessment Methods' and 'Additional Notes' above.
||Hours & Minutes
|Main Exam Diet S2 (April/May)||Derivatives Markets and Derivative Pricing & Financial Modelling||3:00|
| On completion of this course the student should be able to:
- demonstrate an understanding of the theoretical frameworks for pricing derivatives, including the Black-Scholes model;
- demonstrate an awareness of the differences between the real-world and the risk-neutral probability measures;
- derive the underlying theory for pricing bonds and interest-rate derivatives;
- show their critical understanding of the assumptions underlying common models of asset process and interest rates;
- show a conceptual understanding of the processes in pricing derivative securities to enable the wider application of knowledge in different and new contexts;
- calculate approximate prices for European and American-style derivatives using the binomial model;
- use the Black-Scholes formula to tackle appropriate problems;
- demonstrate how to price and hedge simple equity derivatives contracts;
- demonstrate how the Greeks can be used to manage the risk in a portfolio of derivatives;
- apply the main models for the term-structure of interest rates for pricing bonds and interest-rate;
- find problem solutions in groups;
- plan and organize self-study and independent learning;
- use programming tools in the application of pricing methods;
- communicate effectively problem solutions to peers.
|Etheridge, A. (2002). A Course in Financial Calculus. CUP.|
Cairns, A.J.G. (2003). Interest Rate Models: An Introduction. Princeton University Press.
Hull, J.C. (2002). Options, Futures and Other Derivatives (5th Edition). Prentice-Hall.
Lamberton, D. & Lapeyre, B. (1996). Introduction to Stochastic Calculus Applied to Finance. Chapman & Hall.
Bingham, N.H. & Kiesel, R. (2004). Risk-Neutral Valuation. Pricing and Hedging of Financial Derivatives. Springer.
|Graduate Attributes and Skills
|Course organiser||Dr David Siska
Tel: (0131 6)51 9091
|Course secretary||Ms Hannah Burley
Tel: (0131 6)50 4885