Constant Elasticity of Variance Option Pricing Model With Time-Dependent Parameters

Abstract

This paper provides a method for pricing options in the constant elasticity of variance (CEV) model environment using the Lie-algebraic technique when the model parameters are time-dependent. Analytical solutions for the option values incorporating time-dependent model parameters are obtained in various CEV processes with different elasticity factors. The numerical results indicate that option values are sensitive to volatility term structures. It is also possible to generate further results using various functional forms for interest rate and dividend term structures. Furthermore, the Liealgebraic approach is very simple and can be easily extended to other option pricing models with well-defined algebraic structures.

Optimal portfolios for DC pension plans under a CEV model

“…doi:10.1016/j.insmatheco.2009.01.005 is negative. The CEV model was usually applied to calculating the theoretical price, sensitivities and implied volatility of options, see e.g., Cox (1996), Lo et al (2000), Davydov and Linetsky (2001), Detemple and Tian (2002), Yuen et al (2001), Jones (2003) and Widdicks et al (2005). Recently, however, Xiao et al (2007) began to apply the CEV model to the pension investment and derived the dual solution for the logarithm utility via a Legendre transform and dual theory.…”

An extended CEV model and the Legendre transform–dual–asymptotic solutions for annuity contracts

“…Note that in the CEV model the elasticity parameterβ is a negative which has been examined by many authors (e.g., Beckers (1980), Schroder (1989, Cox (1996), Lo and Yuen (2000), Davydov and Linetsky (2001), Yuen et al (2001) and Jones (2003)), and then from Eq. (2.1), we see that the CEV model has the problem of a perpetually declining volatility with the stock increasing.…”

Optimal Investment Problem with Multiple Risky Assets under the Constant Elasticity of Variance (CEV) Model

“…In comparison with other stochastic volatility models, the CEV model is easier to deal with analytically and the GBM model can be seen as its special case. The CEV model was usually applied for option pricing and sensitivity analysis of options in most literatures, see [16][17][18][19] for example. Recently, the CEV model has been applied in the research of optimal investment, as was done by Xiao, Zhai and Qin [20].…”