***COURSE NOW FULL***
Calculus and statistics
Dr Jean-Pierre Zigrand
The course is an introduction to the concepts and models underlying the modern analysis and pricing of financial derivatives, from vanilla calls and puts on stocks to complex exotics in the volatility, correlation and fixed income arenas. The underlying philosophy of the course is to first provide the firm foundations for understanding derivatives in general, rather than following a cooking-book approach. 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, contributing to beneficial financial engineering innovations as well as to the potential of financial crises. Daily assignments complement the lecture material.
The first half of the course will be taught by Jean-Pierre Zigrand. This part deals mainly with 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, taught by Andrea Vedolin 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.
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, (8th edition), Pearson, (2011).
Robert McDonald, Derivatives Markets, (3rd edition), Pearson, (2009).
K. Redhead, Financial Derivatives, Prentice Hall, (1997).
Lectures: 36 hours Classes: 12 hours
Assessment: Two written examinations