Mathematics 797FR - ST-Financial Math & Risk Mngt

This is the second course of the series. We will introduce the concepts of arbitrage, state price densities and equivalent martingale measures. European and American claims. Optimal stopping. We will study admissible strategies, pricing and hedging in Markovian models. Admissible strategies. Pricing and hedging in Markovian models. We will consider different ways of of modeling markets with uncertain volatility. We will cover stochastic volatility models, auto-regressive models as well as recently derived nonlinear pricing models. We will emphasize, in particular, worst-case scenario risk-management techniques, and managing volatility risk with options. The main probability tool we will use is the Extreme Value Theory. Finally, we will cover more practical risk-management techniques and guidelines such as the "Value at Risk" outlined in the J.P. Morgan technical document on measuring financial risk.

Open to Graduate students only. Note: MATH 797SC - ST-Adv. Stochastic Calculus is a pre-requisite to this course.