Aims:
To introduce, in a discrete time setting, the basic probabilistic ideas and results needed for the conceptual understanding of the theory of stochastic process and its application to financial derivative pricing.
Summary:
- Introduction to background probability theory.
- Conditional expectation.
- Discrete-time martingales, sub- and supermartingales.
- Stopping Times, Optional Stopping Theorem, Snell Envelopes.
- Arbitrage and martingales, risk neutral measures.
- Complete markets and discrete option pricing.
- The binary tree model of Cox, Ross and Rubinstein for European and American option pricing.
- Dividends in the binomial models.
Detailed Information
Course Description: Link to Official Course Descriptor.
Pre-requisites: none.
Location: Edinburgh.
Semester: 1.
Learning Outcomes:
It is intended that students will demonstrate:
- conceptual understanding of conditional expectations,
- thorough understanding of the Cox-Ross-Rubinstein binomial model and its application to option pricing problems,
- conceptual understanding of the role of the risk-neutral pricing measure,
- conceptual understanding of the role of equivalent martingale measures in financial mathematics,
- conceptual understanding of the Optional Stopping problem
by answering relevant exam questions.
Reading list:
The students are referred to the following texts.
- Williams, D. (1991). Probability with Martingales. CUP.
- Bingham, N.H. & Kiesel, R. (2004). Risk-Neutral Valuation. Pricing and Hedging of Financial Derivatives. Springer.
- Baxter, M. & Rennie, A. (1996). Financial Calculus. CUP.
- Lamberton, D. & Lapeyre, B. (1996). Introduction to Stochastic Calculus Applied to Finance. Chapman & Hall.
SCQF Level: 11.
Credits: 10.
Other Information
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