Course co-ordinator(s): Dr Timothy C Johnson (Edinburgh).
Aims:
The aims of this module are:
- To provide a thorough grounding in financial engineering (the including non-vanilla derivatives, securitisation and structuring)
- To introduce mathematical concepts hedging and pricing derivatives
- To provide students with a good understanding of developing the BSM model to different asset classes,
- To provide students with an understanding of pricing American options
- To provide students with a good understanding of exotic options
- To provide students with a good understanding of modelling interest rates, including Libor Market Models and valuing swaptions
- To introduce the student to securitisation
- To provide students with an understanding of managing a complex portfolio of assets
Detailed Information
Pre-requisites: none.
Location: Edinburgh.
Semester: 2.
Syllabus:
1. Stochastic Calculus applied to financial markets
- The Martingale Approach to asset pricing, including Cameron-Martin-Girsanov Theorem, the concept of the Radon-Nikodym derivative, the Martingale Representation Theorem
- Self-financing portfolios in continuous time and the construction of replicating strategies using the martingale approach
- OU and Feller processes and derivation of a BSM like PDE
- The role of the market price of risk in the transfer between the real-world and the risk-neutral probability measures
- Hedging derivatives and the Greeks in continuous time models and to structures
2. Volatility
- The role of the volatility parameter in the valuation of options
- Estimation of volatility from market data
- The “smile” effect and volatility surfaces
3. Exotic options, derivative portfolios and securitisation
- Description of exotic options (including Quanto, Chooser, Barrier, Binary, Lookback Asian, Exchange, Basket options)
- Swaps and swaptions
- Securitisation, Structured Derivatives and Synthetic Securities
- Risk Management of portfolios/securitised assets.
4. Modelling the Term Structure of Interest Rates
- The Black, Hull & White Vasicek and Cox-Ingersoll-Ross models (Ho & Lee, Black, Derman & Toy, Black & Karasinski)
- HJM framework.
- Libor Market Models
- Implementation and calibration of models
5. Financial Engineering Project
- Extended project synthesising knowledge in a practical setting.
Reading list:
Hull (2011). Options, Futures and Other Derivatives, 8th edition. Prentice Hall.
Baxter and Rennie (1996). Financial calculus. Cambridge University Press.
Duhon, T. (2013). How the trading floor really works. Wiley/Bloomberg.
Jarrow and Chaterjea (2013). An Introduction to Derivative Securities, Financial Markets and Risk Management. W. W. Norton & Co.
Langtangen, H. P. (2009). A Primer on Scientific Programming with Python. Springer.
Assessment Methods:
40% through coursework, 60% through end of semester exam.
SCQF Level: 11.
Credits: 15.
Other Information
Help: If you have any problems or questions regarding the course, you are encouraged to contact the lecturer
VISION: further information and course materials are available on VISION