SC²S Colloquium - July 26, 2012

Date:	June 26, 2012
Room:	02.07.023
Time:	3 pm, s.t.

Samuel Maurus: A multi-dimensional PDE solver for option pricing based on the Heston model and sparse grids

The pricing of non-trivial financial options must in general be performed using numerical techniques. This thesis presents a practical implementation of a deterministic option-equation solver based on Heston's stochastic volatility model - a model which generalises on that of Black-Scholes. The solver uses a finite-element approach based on sparse grids for spatial discretisation. Grid adaptivity is used to refine sensitive regions in the problem space. The solver supports the pricing of European basket call and put options without the drawback of slow convergence that typically accompanies non-deterministic techniques.

Results from the solver for vanilla options are provided and compared to Heston's closed-form solution as well as to an existing numerical solver (based on the Black-Scholes model). Results for basket options with up to three underlyings (problem dimensionality of six) are also provided and compared with existing Monte-Carlo results. Conclusions are made on the applicability of the solver and recommendations for further work in the area are given.