Valuation of Options under Heston Stochastic Volatility Model Using Wavelets

The paper is concerned with option pricing using the Heston stochastic volatility model. The Heston model is represented by parabolic boundary value problem. We use theta scheme for semidiscretization in time and we propose an adaptive wavelet method for solving the boundary value problem on the given time level. Furthermore, we construct a quadratic spline wavelet basis that is adapted to homogeneous Dirichlet boundary conditions on the part of the boundary and Neumann boundary conditions on the remaining part. The main advantage of the method is that the approximate solution is represented by small number of parameters. A numerical example is presented for a European call option.