This class teaches how to price and hedge vanilla and exotic derivatives based on the fundamental principles of arbitrage. Some of the key concepts of the class are: pricing, hedging, replication, simulation, optimal stopping, smile, volatility surface, Greeks, Gaussian and non-Gaussian models.
Here are the main topics covered: description of main derivatives products and strategies, Black Scholes formula, American options with binomial trees, path-dependent options with Monte-Carlo simulations, arbitrage-free relations, futures and forwards, options on indices, currencies and futures, limits of the Black and Scholes theory, the smile and the volatility surface, Heston’s model, applications to corporate finance.
This class is technical in essence. It alternates between formal developments (mathematical proof of the Black and Scholes formula,…), exercises, and a lot of programming in VBA. Homework consists in designing a pricer similar to those found on the desks of investment banks.
Students will learn useful tricks concerning derivatives for the Series 7 license. The knowledge gained in this class is also useful for SOA exam MLC and the FRM and CFA exams. Students should read the book by John Hull: Options, Futures and Other Derivatives, Pearson, at home in parallel with the class.