High-order compact scheme for solving nonlinear Black–Scholes equation with transaction cost

In this paper, an unconditionally stable high-order compact finite difference scheme is proposed. The compact scheme is fourth-order accurate in both the temporal and spatial dimensions. The new method computes both the option price and the hedging delta ∂ V/∂ S simultaneously. Two numerical examples are presented to demonstrate the accuracy and efficiency of the proposed scheme.

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