Abstract
AbstractThe inclusion of nonzero transaction costs in option pricing invalidates the Black–Scholes hedging strategy that relies on continuous rebalancing of the option portfolio. Based on Leland's approach of discrete hedging, this paper presents complementarity based numerical methods for the pricing of American options in the presence of transaction costs. The American option pricing models with transaction costs are formulated as partial differential complementarity problems, which are discretized by finite-difference schemes. The resulting discretized finite-dimensional linear and nonlinear complementarity problems are shown to have solutions, which are computable by iterative complementarity methods. Numerical results are reported.
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