The course delivers the concepts and models underlying the modern analysis and pricing of financial derivatives. The underlying philosophy of the course is to first provide the firm foundations for understanding derivatives in general.
The required technical tools will be explained carefully, allowing students to learn the language and to be able to converse with derivatives professionals. Once the tools are in place, those same tools can then be applied to any derivative. Special emphasis will be put on those derivatives that shape the modern world.
Topics covered include:
Arbitrage and Risk-Neutral Pricing
Basic Properties of Forwards and Options
The Binomial model of Cox, Ross and Rubinstein
A primer on Stochastic Calculus and continuous-time modeling
The Model of Black and Scholes
Greeks and Hedging Schemes
Forwards and Futures
Exotic and Path-Dependent Options, Structured Products
Historical Volatility, Implied Volatility and Heston’s Stochastic Volatility model
Variance and Correlation Swaps
Introduction to Fixed-Income and Interest Rate derivatives
Interest Rate Options
The first half of the course involves the review of the required tools, the setup of the pricing framework, the intuition of the methodology and the application to plain vanilla derivatives.
The second half of the course applies those techniques to more advanced topics: exotic derivatives, volatility modelling (including stochastic volatility, local volatility and volatility derivatives such as variance swaps) and interest-rate derivatives.
As far as mathematics go, the student should feel comfortable with calculus, probability and statistics at the intermediate undergraduate level. The two main mathematical tools used repeatedly in this course are: the expectation (integration) of random variables and the second-order Taylor expansion (which underpins Ito's Lemma). A prior review of such concepts would be fruitful. Prior knowledge of stochastic calculus is not required.
World-class LSE teaching
The LSE’s Department of Finance has grown in recent years to become one of the largest and most highly-regarded finance groups in the UK and Europe. On this three week intensive programme, you will engage with and learn from full-time lecturers from the LSE’s finance faculty. FM360 course lecturers, Dr Jean-Pierre Zigrand and Dr Rohit Rahi, teach on a number of our undergraduate and graduate Finance modules, including Financial Engineering, Advanced Asset Pricing, and Derivatives.
The main reading material will be the detailed handouts distributed at the beginning of the course. Optionally, the following MBA-level books are standard textbooks in the financial industry:
J.C. Hull, Options, Futures and Other Derivatives, 9th edition, Pearson (2015).
R.L. McDonald, Derivatives Markets, 3rd edition, Pearson (2013).
K. Redhead, Financial Derivatives, Prentice Hall (1997).
P. Veronesi, Fixed Income Securities, Wiley (2010).
*A more detailed reading list will be supplied prior to the start of the programme
**Course content, faculty and dates may be subject to change without prior notice