The numerical approximation of nonlinear Black–Scholes model for exotic path-dependent American options with transaction cost

In this paper, a new second-order exponential time differencing (ETD) method based on the Cox and Matthews approach is developed and applied for pricing American options with transaction cost. The method is seen to be strongly stable and highly efficient for solving the nonlinear Black–Scholes model. Furthermore, it does not incur unwanted oscillations unlike the ETD–Crank–Nicolson method for exotic path-dependent American options. The computational efficiency and reliability of the new method are demonstrated by numerical examples and by comparing it with the existing methods.

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