Pricing derivatives in stochastic volatility models using the
finite difference method
The Heston stochastic volatility model is one extension of the Black-Scholes
model which describes the money markets more accurately so that more
realistic prices for derivative products are obtained.
From the stochastic differential equation of the underlying
financial product a partial differential equation (p.d.e.) for the value
function of an option can be derived. This p.d.e. can be solved with
the finite difference method (f.d.m.). The stability and consistency
of the method is examined. Furthermore a boundary condition is proposed
to reduce the numerical error. Finally a non uniform structured grid
is derived which is fairly optimal for the numerical result in the
most interesting point.
An online version of the programme which uses the finite difference
method to determine prices of options with the Heston stochastic
volatility model is available. A slightly different version of that
programme is developed and examined within the diploma thesis.