|
Description:
|
This course considers more advanced models. We start by revisiting the Fourier transform and discuss how to use this technique to price vanilla options in different standard vol models (Heston, Hull and White and Stein & Stein). We then study the theory of jump processes including Ito's lemma and Girsanov's theorem. We first focus on the Poisson process and the compounded Poisson. We then explain how to create the family of Cox-processes, which plays an important role in the credit derivatives' literature. Subsequently, we apply this theory to build asset pricing models, such as Bates' model (this is basically Heston's model with jumps added). If time permits, we will look at commodities and their derivatives. We will describe how the before mentioned models can be be adjusted price such derivatives. We will not follow a textbook but one useful reference is: J. Gatheral, The Volatility Surface: A Practitioner's Guide, Wiley, 2006. Prerequisite: Stochastic Calculus for Finance II 46-945, Simulation Methods for Option Pricing 46-932.
|
