- Lecture Notes / Slides
- Examples / Solutions
- Reading List / Past Papers
Lecture notes for the course will appear here on Wednesdays for the following week.
Introducing the course is taught, what is to be expected and how it is assessed. We introduce some elementary economics including the time value of money and models for stock prices.Download
2. Properties of SDEs
Some general properties of SDEs are introduced. The extremely important Ito's lemma is quoted.Download
Introducing simple financial derivative contracts, and how they are combined to create portfolios.Download
5. Trading with Portfolios
Trading strategies. Some further market descriptions such as bonds and the no-arbitrage principle.Download
Upper and Lower Bounds on Put Options. Proof of Put-Call Parity by No-Arbitrage Principle. Example on Arbitrage OpportunityDownload
8. One Step Binomial
One-Step Binomial Model for Option Price. Risk-Neutral Valuation. Examples.Download
10. Multi-Period Binomial Trees
Binomial Model for Stock Price. Option Pricing on Binomial Tree. Matching Volatility σ with u and dDownload
11. American Option and Replicating Portfolio
American Put Option Pricing on Binomial Tree. Replicating PortfolioDownload
13. Boundary Conditions and the Black-Scholes Formula
Boundary Conditions for Call and Put Options. Exact Solution to the Black-Scholes Equation and limiting solutions.Download
16. Dividends and Early Exercise
How to modify the BS equation for dividends and early exercise options.Download
17. Pricing Bonds
Bond pricing with interest rates and coupon payment rates as known functions of time.Download
Examples and solutions for the course will appear here on Fridays.
Examples Sheet 3
No Arbitrage Principle, Upper and Lower Bounds: Examples to accompany lectures 6 to 7.Download
Example Sheet 5
American Put Option, Replicating Portfolio and Arbitrage: Examples to accompany lecture 11.Download
Reading list for the course.
The Mathematics of Financial Derivatives
Wilmott, P., Howison, S., Dewynne, J., "The Mathematics of Financial Derivatives", Cambridge University Press, (1995) ISBN: 0521497892
Options, Futures and other Derivatives
Hull, J. C., 2011: "Options, Futures and other Derivatives", 8th edition, Prentice Hall. ISBN: 0132777428.
Please follow the link for podcasts of the lecture, the written additions to the notes will be recorded there. If you log onto Blackboard, the discussion forum can be found under the communication tab. If you are already logged in follow the link below. I will try to answer any queries or emails on the forum.