Haar wavelet-based valuation method for pricing European options

A numerical method based on the Haar wavelet is introduced in this study for solving the partial differential equation which arises in the pricing of European options. In the first place, and due to the change of variables, the related partial differential equation (PDE) converts into a forward time problem with a spatial domain ranging from 0 to 1. In the following, the Haar wavelet basis is used to approximate the highest derivative order in the equation concerning the spatial variable. Then the lower derivative orders are approximated using the Haar wavelet basis. Finally, by substituting the obtained approximations in the main PDE and doing some computations using the finite differences approach, the problem reduces to a system of linear equations that can be solved to get an approximate solution. The provided examples demonstrate the effectiveness and precision of the method.