Occurrence | Teaching period |
---|---|
A1 | Semester 1 2024-25 |
A2 | Semester 1 2024-25 to Semester 2 2024-25 |
B1 | Semester 2 2024-25 |
B2 | Semester 2 2024-25 to Semester 1 2025-26 |
The aim of the module is to explain in simple - namely discrete time - settings the fundamental ideas of modelling of financial markets and pricing of derivative securities using the principle of no arbitrage. Even the simplest of all models with only one time step allows several important notions to be illustrated. The module progresses with more complex models - involving many time steps and several stocks - which are developed along with the corresponding theory of pricing and hedging derivative securities such as options or forwards. Relatively simple mathematical considerations lead to powerful notions and techniques underlying the theory - such as the no-arbitrage principle, completeness, self-financing and replicating strategies, and equivalent martingale measures. These are directly applicable in practice, particularly in the continuous time limiting theory developed in a subsequent module. The general methods are applied in detail in particular to pricing and hedging European and American options within the Cox-Ross-Rubinstein (CRR) binomial tree model. The Black-Scholes model as the limit of CRR models is discussed to pave the way for continuous time theory.
By the end of this module students should
Task | % of module mark |
---|---|
Coursework - extensions not feasible/practicable | 100 |
Oral presentation/seminar/exam | 0 |
None
Task | % of module mark |
---|---|
Coursework - extensions not feasible/practicable | 100 |
Oral presentation/seminar/exam | 0 |
Information currently unavailable
1. M. Capinski and E. Kopp, Discrete Models of Financial Markets, Cambridge University Press 2012.
2. M. Capinski and T. Zastawniak, Mathematics for Finance: An Introduction to Financial Engineering, 2nd edition, Springer 2011.
3. R. Elliott, E. Kopp, Mathematics of Financial Models, Springer 2005.
4. J. van der Hoek, R. Elliott, Binomial Models in Finance, Springer 2005
5. D. Lamberton, B. Lapayere, Introduction to Stochastic Calculus Applied to Finance, Chapman & Hall 2008.
6. A. Etheridge, A Course in Financial Calculus, Cambridge University Press, 2002.