Pricing American Options under the Constant Elasticity of Variance Model and Subject to Bankruptcy

Abstract

This paper proposes an alternative characterization of the early exercise premium that is valid for any Markovian and diffusion underlying price process as well as for any parameterization of the exercise boundary. This new representation is shown to provide the best pricing alternative available in the literature for medium-and long-term American option contracts, under the constant elasticity of variance model. Moreover, the proposed pricing methodology is also extended easily to the valuation of American options on defaultable equity and possesses appropriate asymptotic properties.

Pricing and static hedging of American-style options under the jump to default extended CEV model

“…Our numerical results show that the SHP methodology is more efficient (and as accurate as) the optimal stopping approach of Nunes (2009).…”

“…However, and in opposition to the standard geometric Brownian motion case, such an extension does not offer an analytic representation for the integral equation representing the early exercise premium, which undermines its computational efficiency. Based on the optimal stopping approach of Bensoussan (1984) and Karatzas (1988), Nunes (2009) proposes an alternative characterization of the standard American-style option price that is valid for any continuous representation of the exercise boundary and for any Markovian price process describing the dynamics of the underlying asset price, including the jump to default constant elasticity of variance (JDCEV) model of Carr and Linetsky (2006). Chung and Shih (2009) tackle the American-style option pricing problem through the static hedge approach (hereafter, SHP) initially developed by Bowie and Carr (1994), Der-man et al (1995), and Carr et al (1998) for hedging European-style exotic options (in which case the boundary is known ex-ante).…”

“…Second, we extend the optimal stopping approach of Nunes (2009) for the pricing of American-style capped options, assuming that the recovery value associated to the put can be paid at the default time-as in Nunes (2009, Section VII)-or at the maturity date of the option. Our numerical results show that the SHP methodology is more efficient (and as accurate as) the optimal stopping approach of Nunes (2009).…”

“…As argued in Nunes (2009Nunes ( , page 1250, the optimal stopping approach offers a better speedaccuracy trade-off than the pricing methodology of Detemple and Tian (2002)-which is based on the (very time consuming) full recursive method of Huang et al (1996)-and the accelerated recursive scheme of Kim and Yu (1996), for valuing option contracts under the CEV assumption. Therefore, the accuracy and efficiency of the SHP approach for valuing American-style options under the CEV model will be compared against the option pricing framework proposed by Nunes (2009).…”

“…Therefore, the accuracy and efficiency of the SHP approach for valuing American-style options under the CEV model will be compared against the option pricing framework proposed by Nunes (2009).…”