Options and Volatility Products

Undergraduate / Graduate

This class covers the pricing and hedging of different type of financial options, as well as of volatility products. The class will develop the analytical tools necessary to understand the basic properties of prices and hedging portfolios, and to write computer code for the valuation and hedging of a very large class of derivatives. The first part of the course covers the valuation of European and American options on Stocks, Commodities, Futures. The second step is to extends it to arbitrary derivative contracts. We will start with the binomial model, and then we will introduces its continuous time limit, as in Black-Scholes. We will proceed to study the valuation of an arbitrary general derivative where the underlying follows a continuous time process. We will further extend it to the case where the derivative depends on several stochastic process, which is required for some cases such as interest rate products, exotic options, and most importantly stochastic volatility. The last part of the class develops the theory of volatility products, with emphasis on variance and volatility swaps, the role of VIX, and derivatives written on VIX over them.