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 Brownian-based models (Heston 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). We will not follow a textbook but one useful reference is: J. Gatheral, The Volatility Surface: A Practitioner's Guide, Wiley, 2006.
Lecture: 100min/wk and Recitation: 50min/wk