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This paper proposes an accelerated static replication approach for continuous European-style barrier options by employing the repeated Richardson extrapolation technique with the Romberg sequence. This approach is developed under the constant elasticity of variance (CEV) model of Cox (1975) and Cox and Ross (1976) using the framework offered by Derman, Ergener, and Kani (1995; DEK) and its modified method of Chung et al. (2010, 2013a, 2013b) andTsai (2014). The numerical results indicate that our method could significantly reduce replication errors for European knock-out call options and may be superior to the imposition of the theta-matching condition on the DEK method.

This article provides a general accelerated recursive integration method for pricing American options based on stochastic volatility and double jump processes. Our proposed model is a generalization of the recursive integral representation method. American option prices can be evaluated by the sum of a corresponding European option price and an early exercise premium integral. Numerical results show that our proposed method is efficient and accuracy in pricing American options with stochastic volatility and double jump processes. © 2015 Wiley Periodicals, Inc. Jrl Fut Mark 36:887–901, 2016

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