Prerequisite: Exposure to relevant concepts at undergraduate level and instructor consent. The only requirement for this course is that either you are doing IE 621 (or equivalent) along with course or have already done such a course. Probability background is not required in the first half, but will be useful for the second half of the course.
The aim of this course is to cover some basic concepts of financial engineering: the issues that arise in modeling, analysis and decision making involving financial instruments. Discrete time models and computational tools will be the focus.
Portfolio optimization: Markowitz model; Two and one fund theorems; mutual funds. Capital Asset Pricing model; Security market line.
Arbitrage; Hedging; Pricing. Contingent claims; Forward and futures contracts. European and American options; Asian and other path dependent options. One and multi-period binomial models; Finite state models. Equivalent martingale measures; Completeness of markets; Fundamental asset pricing theorems; Option pricing. Black-Scholes option pricing formula.
- M Capinski and T. Zastawniak (2003), Mathematics for Finance: An Introduction to Financial Engineeting and Springer-Verlar, London.
- D. G. Luenberger (1998), Investment Science, Oxford University Press, New York
- J. C. Hull (2000), Options, Futures and other Derivatives, Fourth edition, Prentice Hall Inc., Upper Saddle River
- D Lamberton and B Lapeyre (1996), Introduction to stochastic calculus applied to finance, Chapman and Hall, London.