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The numerical valuation of European two-asset options is considered under the Black–Scholes model. A numerical method is discussed based on FD discretization of the pertinent PDE on nonuniform grids and subsequent discretization in time by ADI schemes. We investigate stability and convergence experimentally for both the option value function and the Cross Gamma function, which is important to nonlinear extensions of the model, beyond the standard Black–Scholes framework.

Numerical solution of a two-asset option valuation PDE by ADI finite difference discretization