Head of Risk Analytics for Global Markets
Bank of America Merrill Lynch
The Second Quantization of Banks
• From derivatives pricing to portfolio modelling
• From bilateral to multilateral risks and network effects
• From the risk neutral world to the real world
• From efficient markets to inefficient markets
• Process automation and optimisation
• Quantitative data analysis
Christoph Burgard heads the Risk Analytics team for Global Markets at Bank of America Merrill Lynch, which he joined in November 2015. Prior to this he spent 16 years at Barclays, where he was leading the Equity Derivatives and XVA front office Quantitative Analytics teams for the investment bank as well as the ALM modelling area for the bank’s treasury department.
Christoph was named Risk Magazine’s Quant of the Year 2015 for his pioneering work on FVA. He has a PhD in Particle Physics from Hamburg University and was a research fellow at CERN and DESY.
University of Delft
Symposium on Numerical Methods:
On an efficient one and multiple time-step Monte Carlo simulation of the SABR model
In this work, we propose an efficient Monte Carlo simulation for the SABR model. The technique is based on an efficient simulation of SABR’s integrated variance process. The integrated variance process appears in the SABR model simulation since it is part of the conditional cumulative distribution of the SABR forward asset dynamics. We base our approach on the derivation of the cumulative distribution function of the integrated variance and the use of a copulas to approximate the conditional distribution
(integrated variance conditional on the SABR volatility process). For that, a recursive procedure based on Fourier numerical techniques recovers the probability density function given the corresponding characteristic function. Resulting is a fast and accurate simulation algorithm. The one time-step version can be employed to price European options under the SABR dynamics. This converts this approach into an alternative to Hagan analytic formula for short maturities and calibration procedures. On the other hand, the multiple time-step extension of our technique is specially useful for long-term options and for exotic options.
Álvaro Leitao is a PhD student at the Delft Institute of Applied Mathematics (DIAM) in the Delft University of Technology and a PhD researcher at Scientific Computing department in the National Center of Mathematics and Computer Science (CWI), under the supervision of Prof. Cornelis W. Oosterlee. His research is focused on hybrid Monte Carlo-based methods and the application of the GPU computing in the computational finance context. Particularly, he is interested in efficient techniques for the
Before his PhD research period, he worked at Department of Mathematics in University of A Coruna, also on the application of high-performance computing to SABR-like models.
Currently, his research interest moves to the use of Machine Learning within the computational finance framework.