Fast solver for Heston and Hull/White model

Floris Naber

Site of the project:
ING Bank
Foppingadreef 7
1102 BD Amsterdam

start of the project: December 2006

In March 2007 the Interim Thesis has been appeared and a presentation has been given.

The Master project has been finished in September 2007 by the completion of the Masters Thesis and a final presentation has been given. For working address etc. we refer to our alumnipage.

Summary of the master project:
In 1973, Myron Scholes and Fischer Black presented a model to predict option prices (Black-Scholes equation). Until then only a small amount of options was traded, but thereafter the option trade increases considerably. The Black-Scholes equation is a simple partial differential equation, due to a number of assumptions, which are used to derive the model. Fischer Black already noted that the assumptions lead to an unrealistic model. A number of people have tried to relax these restrictions in order to obtain better models. It appears from the data that the volatility and the interest are not constant, but vary in an arbitrary way. If the volatility and the interest are stochastic, the 1 dimensional partial differential equation is replaced by a 3 dimensional partial differential equation (for this derivation the Feynman-Kac formula is used). The straigthforward numerical solution of this equation consumes a lot of computer time and memory. So, there is an urgent need to invent more efficient methods.

The aim of this master project is to develop an efficient method to solve the 3 dimensional partial differential equation. In particular the investigation is focussed on the Hull-White Heston partial differential equation (Hull-White Heston is a model with stochastic volatility and the interest. This partial differential equation has been derived by using the Feynman-Kac formula).

Contact information: Kees Vuik

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