Abstract
The semi-analytical valuation of CEV American options is either computationally expensive when it delivers sufficiently accurate prices, lacks accuracy when computations are faster, or involves functions whose computations can be unstable. Trinomial schemes have the disadvantage that there are no built-in ways to compute hedging sensitivities and re-runs are required for the computation of deltas and gammas. We propose a faster computational technique by discretizing the no-arbitrage partial differential equation using a high-order three-point (compact) finite difference approximation combined with a simple extrapolation process in time. This new CEV American option pricing algorithm is simple to implement and is shown to yield prices with high accuracy. The superiority of the procedure over existing schemes is numerically demonstrated.
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