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.


diploma thesis


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.



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