The Binomial CEV Model and the Greeks

Abstract

This article compares alternative binomial approximation schemes for computing the option hedge ratios studied by Chung and Shackleton (2002), Chung, Hung, Lee, and Shih (2011), and Pelsser and Vorst (1994) under the lognormal assumption, but now considering the constant elasticity of variance (CEV) process proposed by Cox (1975) and using the continuous‐time analytical Greeks recently offered by Larguinho, Dias, and Braumann (2013) as the benchmarks. Among all the binomial models considered in this study, we conclude that an extended tree binomial CEV model with the smooth and monotonic convergence property is the most efficient method for computing Greeks under the CEV diffusion process because one can apply the two‐point extrapolation formula suggested by Chung et al. (2011). © 2016 Wiley Periodicals, Inc. Jrl Fut Mark 37:90–104, 2017

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

“…For instance, given the absence of closed-form solutions of deltas for a general β parameter, Chung and Shih (2009) only consider the case of β = 4/3 for pricing American options to simplify their numerical analysis with the SHP approach. When β = 4/3, Schroder (1989) observes that the analytical expression for the corresponding delta can be determined by using the same type of algebra as in the Black-Scholes (1973) and Merton (1973) Cruz and Dias (2017) remark that the importance of the CEV model for practitioners is justified by its ability to accommodate the leverage effect and the implied volatility skew. 6 The former denotes an inverse relation between stock returns and realized volatility.…”

“…L. Chang, Guo, and Hung (2016) also employ a three-point Richardson extrapolation in their pricing formulae for American-style options. Cruz and Dias (2017) also use the Richardson extrapolation formula to enhance the accuracy of Greeks computed by an extended tree binomial CEV model. 2 However, while Richardson extrapolation succeeds in deriving efficient approximation formulae in the literature, its application in static replication has seldom been explored.…”

Computing the CEV option pricing formula using the semiclassical approximation of path integral

“…In order to deal with these problems, many approaches have been reported for the European-vanilla type option pricing. These approaches include numerical schemes [25,[27][28][29], Montecarlo simulations [30], perturbation theory model [31], and analytical approximations to the transition density [32] or to the hedging strategy [33], among others.…”