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The objective of this course is to develop necessary skills to value and hedge a wide variety of derivative contracts traded in financial markets. The main tool of analysis of the course is stochastic calculus set in continuous time. Some basic knowledge of stochastic processes would be helpful, but not essential: what needed will be covered in class. The analytic valuation and hedging of derivatives using the modern martingale methods will be the main focus of the course. Applications will include forwards, futures, and options on stocks, bonds and foreign currencies. The numerical methods such as parameter estimation, Monte Carlo simulations, discretization schemes as well as the conditional volatility estimation techniques will also be addressed. In addition to the valuation and hedging derivatives, course also covers Value-at-Risk, credit risk, modeling the term structure of interest rates and the construction of the VIX index using the S&P 500 index options obtained from the IvyDB OptionMetric database.

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