Alok Gupta
Mathematical Institute
University of Oxford
24-29 St Giles'
Oxford
OX1 3LB
UK
Hertford College
University of Oxford
Catte Street
Oxford
OX1 3BW
UK
I am DPhil student working in the Mathematical and Computational Finance Group (MCFG) which is part of the Mathematical Institute at the University of Oxford. I have recently submitted my full DPhil thesis and am expecting to viva in the first quarter of 2010. My research is funded by a CASE Award made jointly between the UK Engineering and Physical Sciences Research Council (EPSRC) and Nomura Bank through the Nomura Centre for Mathematical Finance. My supervisor is Dr Christoph Reisinger and I am a Senior Scholar at Hertford College.
As part of my research I am currently considering a Bayesian approach to calibrating financial models. In particular I look at recovering generating the local volatility surface. I work in a general non-parametric framework and use Bayesian priors for the surface in order to regularise and smooth the solution. It is hoped this will lead to a distribution of prices for more exotic options and hence some measure of the uncertainty in the prices and risk. I prove some general consistency properties for the Bayesian estimators and derive new model uncertainty measures.
In addition I look at using the full information of the posterior distribution of calibrated parameters to construct optimal Bayesian hedging strategies. In the future I hope to apply this technique to the problem of optimal portfolio selection for a variety of return-risk objectives.
