The analysis of the finite difference schemes with nonuniform meshes for the problems of partial differential equations is extremely rare even for very simple problems and even for the method of fully ...

Based on multiplicative calculus, the finite difference schemes for the numerical solution of multiplicative differential equations and Volterra differential equations are presented. Sample problems ...

A free-boundary formulation is considered for the price of American options under jump-diffusion models with finite jump activity. On the free boundary a Cauchy boundary condition holds, due to the ...

We develop here a finite-difference approach for valuing a discretely sampled variance swap within an extended Black–Scholes framework. This approach incorporates the observed volatility skew and is ...