Postgraduate Course: Stochastic Analysis in Finance II (MATH11077)
|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||This course aims to provide a good and rigorous understanding of the mathematics used in derivative pricing and to enable students to understand where the assumptions in the models break down.
The Black-Scholes model, self-financing strategies, pricing and hedging options, European and American options.
Option pricing and partial differential equations; Kolmogorov equations.
Further topics: dividends, reflection principle, exotic options, options involving more than one risky asset, stochastic volatility models.
Entry Requirements (not applicable to Visiting Students)
||Other requirements|| MSc Financial Mathematics and MSc Financial Modelling and Optimization students only.
Course Delivery Information
|Not being delivered|
| - be able to apply the theory of stochastic calculus to problems involving vanilla options
- understand the martingale representation theorem and its role in financial applications
- be able to apply the theory of stochastic calculus to problems involving exotic options
- conceptual understanding of the role of martingales in the theory of derivative pricing
- conceptual understanding of the role of equivalent martingale measures in financial mathematics
- conceptual understanding of the stochastic Ito integral and the connection to self-financing strategies
|Karatzas, I. & Shreve, S. (1988). Brownian Motion and Stochastic Calculus. Springer.|
Baxter, M. & Rennie, A. (1996). Financial Calculus. CUP.
Etheridge, A. (2002). A Course in Financial Calculus. CUP.
Lamberton, D. & Lapeyre, B. (1996). Introduction to Stochastic Calculus Applied to Finance. Chapman & Hall.
|Graduate Attributes and Skills
||MSc Financial Mathematics and MSc Financial Modelling and Optimization students only.
|Course organiser||Dr Sotirios Sabanis
Tel: (0131 6)50 5084
|Course secretary||Mr Thomas Robinson
Tel: (0131 6)50 4885