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) 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.

Proactive Hedging European Option Pricing with a General Logarithmic Position Strategy

“…For example, stocks do not pay dividends. (5) ere are no transaction costs for buying or selling the underlying assets. (6) e risk-free interest rate is constant over time.…”

“…Options comprise a diverse group of indispensable trading products in the financial market, which make them effective tools for hedging risks. e options currently being traded include more than the standardized European and American options; in fact, a vast number of exotic options (e.g., barrier options, Asian options, lookback options, step options, rainbow options, binary options, and basket options, among others) are being changed, combined, and derived from the standard options [1][2][3][4][5][6][7][8][9][10][11][12].…”

A Cubic B-Spline Collocation Method for Barrier Options under the CEV Model

“…Dias [7] has developed two new methods for pricing and hedging European barrier option contracts under the Jump to Default Extended Constant Elasticity of Variance (JDCEV) model, i.e., the stopping time method based on the first passage time densities of the underlying asset price process through the barrier level, as well as a static hedging portfolio method in which the barrier option is replicated by a portfolio of plain-vanilla and binary options. Guo and Chang [8] proposed an accelerated static replication method for continuous European barrier options by using the repeated Richardson extrapolation technique for Romberg sequences.…”