**
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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