Course Introduction
This course provides a clear understanding of the intuition behind derivatives pricing, how models are constructed, and how they are used and adapted in practice. Strengths and weaknesses of different models. Some important conceptions will be inclueded and tested: Black-Scholes, stochastic calculus, Martingale, exotic options, American options and Greeks.
Both the theory and the practice of the industry-standard pricing models are considered in detail. Each pricing problem is approached using multiple techniques including the well-known PDE and a change of measure.
Schedule
- Review and introduction: assets, portfolio, no-arbitrage, forward contracts, options, binomial model
- Stochastic calculus: Itˆo’s Lemma, geometric brownian motion
- Black-Scholes PDE, delta-hedging
- Martingale pricing: Radon-Nikodym derivative, Girsanov’s theorem, risk-neutral valuation, Black-Scholes formula, change of numeraire
- American options: optimal exercise boundary, linear complementarity problem, free boundary problem, optimal stopping problem, perpetual american put
- Barrier options
- Asian options
- Lookback options
- Multi-asset options: multi-dimensional Itˆo’s lemma, exchange options, cross-currency options, muti-dimensonal Black-Scholes market.
Books
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The Mathematics of Financial Derivatives: A Student Introduction.[see here](http://www.amazon.com/The-Mathematics-Financial-Derivatives-Introduction/dp/ 0521497892)
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Options, Futures, and Other Derivatives, 9th Edition. see here
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Lecture notes of Prof. Touzi and Prof. Tankov at ´Ecole Polytechnique (technical). see here
Preliminary knowledge
You should be familiar with basic concepts of financial derivatives though we will review them in the first lecture. A good introduction is one of the recommended book by John Hull: Options, Futures, and Other Derivatives. You must also have some basic knowledge in multivariable calculus and probability.