Course co-ordinator(s): Dr Torsten Kleinow (Edinburgh).
This course introduces the basics of financial derivatives pricing and delves further into the stochastic modelling of financial assets. The course covers the second half of the material in Subject CT8 of the Institute and Faculty of Actuaries examinations.
We introduce the (discrete time) binomial model and the (continuous time) Black Scholes model, and price contingent claims within these models.
Further into the course, we will look at bond pricing and the term structure of interest rates in an arbitrage-free framework.
Course Description: Link to Official Course Descriptor.
Learning Outcomes: Personal Abilities
At the end of studying this course, students should be able to:
- understand the characteristics and uses of derivative securities in financial markets;
- understand put-call parity, gearing, and the dependence of option prices on underlying variables;
- state the binomial (CRR) and Black Scholes model;
- understand the concepts of replication, hedging, and delta hedging;
- work with martingale measures, and understand their connection with arbitrage free/complete markets;
- apply Itô’s Lemma, the Girsanov theorem and the martingale representation theorem;
- derive the Black-Scholes formula and the Black-Scholes PDE;
- price contingent claims;
- derive relationships between forward interest rates, spot rates and zero-coupon bond prices;
- manipulate explicit bond price formulae for the Vasicek and CIR models, and derive the implied forward rate curves;
- Value credit risky bonds.
The following book is recommended:
- Hull, J., (2006) Options, futures and other derivative securities, 6th ed, Prentice Hall;
Students may also find the following books useful:
- Baxter, M. and Rennie, A. (1996), Financial calculus, Cambridge University Press;
- 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;
Assessment Methods: Due to covid, assessment methods for Academic Year 2021/22 may vary from those noted on the official course descriptor. Please see:
- Maths (F1) Course Weightings 2021/22
- Computer Science (F2) Course Weightings 2021/22
- AMS (F7) Course Weightings 2021/22
SCQF Level: 11.
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