Effective Stochastic Volatility
My name is Mike Felpel and I am a third year PhD student in the Applied Mathematics and Numerical Analysis (AMNA) working group of the University of Wuppertal. I received both my bachelor’s and master’s degree in mathematics from the University of Bonn. My main interest of study is the area of stochastics and probability theory. Therefore, both my theses were focused on stochastic behaviour on interlacing particle systems.
Why I became a PhD student
Following my master’s studies, it was quickly clear to me that I wanted to further expand my knowledge and continue my research in the mathematical area of stochastics. On the other hand, however, I was also interested to experience a more practical and real-world oriented application. Therefore, I decided to switch the subject to a more practical oriented area and continued my studies doing a PhD in financial mathematics.
What I will do during my PhD
During my PhD I focus on the stochastic modelling of capital markets. The goal is to provide an accessible and general framework for a large class of stochastic volatility and variance models, including models such as the SABR, ZABR or Heston model. I analyze the pricing of products, the model calibration as well as a corresponding numerical implementation to provide a practical applicable methodology.
For this I use suitable approximations of the model dynamics to deduce an accessible partial differential equation (PDE) for the underlying probability distributions. This PDE can then be solved using various numerical methodologies. In a first step this approach was used to extend the already known setting for the SABR model to incorporate models of the ZABR type and introduce new types of stochastic volatility models. In a second step, a connection between this methodology and the method of Markovian projection was established and used to consider a multidimensional setting and allow, for example, the pricing of basket products. In a final step this method will be extended to also incorporate local stochastic volatility models.