Mirco Mahlstedt holds a Bachelor degree in Mathematics from the Carl von Ossietzky University Oldenburg. After his graduation in 2009, Mirco joined the Master Program "Finance and Information Management" at the TU Munich and the University of Augsburg. He won the third prize of the Postbank Finance Award. During a research project at the RiskLab at the University of Toronto, Mirco wrote his master thesis on "Pricing of multivariate derivatives with two barriers". Since October 2012, he is doing a Ph.D. at KPMG Center of Excellence in Risk Management.
Computational Methods for Option Pricing – Model reduction and methodological risk
Parametric option pricing and calibration to American options are the corner stones in Mirco’s PhD project.
First step was a numerical investigation of the de-Americanization methodology. This methodology is an in the financial industry popular approach simplifying American option data via binomial tree techniques into pseudo-European option data and thus, calibrating European instead of American options. The results of this study yield the conclusion that the de-Americanization methodology does not perform well for all parameter scenarios in all interest rate environments.
The need of executing recurrent tasks such as pricing, calibration and risk assessment accurately and in real-time, sets the direction to model reduction. The two main pillars are the Chebyshev interpolation and the Reduced Basis Method. Via Chebyshev interpolation the recurrent nature of these tasks is exploited by polynomial interpolation in the parameter space. Identifying criteria for (sub)exponential convergence and deriving explicit error bounds enables to reduce run-times while maintaining accuracy. For the Chebyshev interpolation any option pricing technique can be applied for evaluating the function at the nodal points. The Reduced Basis Method is based on PDE techniques. Here, compared to the high-dimensional basis in the e.g. finite element method, the key idea is to define a problem-adapted lower dimensional basis and therefore, reducing the complexity of numerically solving parametric partial differential equations significantly.
Supervisor: Prof. Dr. Kathrin Glau
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