Repeated Richardson extrapolation and static hedging of barrier options under the CEV model

Abstract

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) and Tsai (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.