Postgraduate Course: Stochastic Analysis in Finance II (MATH11077)
Course Outline
| 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 |
| SCQF Credits | 7.5 |
ECTS Credits | 3.75 |
| 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. |
| Course description |
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.
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | MSc Financial Mathematics and MSc Financial Modelling and Optimization students only. |
Course Delivery Information
| Not being delivered |
Learning Outcomes
- 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
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Reading List
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.
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Additional Information
| Graduate Attributes and Skills |
Not entered |
| Special Arrangements |
MSc Financial Mathematics and MSc Financial Modelling and Optimization students only. |
| Study Abroad |
Not Applicable. |
| Keywords | SAF II |
Contacts
| Course organiser | Dr Sotirios Sabanis
Tel: (0131 6)50 5084
Email: |
Course secretary | Mr Thomas Robinson
Tel: (0131 6)50 4885
Email: |
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