Valuing Time-Dependent CEV Barrier Options

Journal of Applied Mathematics and Decision Sciences, pp. 1-17, 2009

20 Pages Posted: 29 Mar 2008 Last revised: 10 Aug 2009

See all articles by Chi-Fai Lo

Chi-Fai Lo

The Chinese University of Hong Kong

Hoi-Man Tang

The Chinese University of Hong Kong (CUHK)

K. C. Ku

The Chinese University of Hong Kong (CUHK)

Cho-Hoi Hui

Hong Kong Monetary Authority - Research Department

Date Written: June 1, 2009

Abstract

In this paper we have derived the analytical kernels of the pricing formulae of the CEV knockout options with time-dependent parameters for a parametric class of moving barriers. By a series of similarity transformations and changing variables, we are able to reduce the pricing equation to one which is reducible to the Bessel equation with constant parameters. These results enable us to develop a simple and efficient method for computing accurate estimates of the CEV single-barrier option prices as well as their upper and lower bounds when the model parameters are time-dependent. By means of the multi-stage approximation scheme, the upper and lower bounds for the exact barrier option prices can be efficiently improved in a systematic manner. It is also natural that this new approach can be easily applied to capture the valuation of other standard CEV options with specified moving knockout barriers. In view of the CEV model being empirically considered to be a better candidate in equity option pricing than the traditional Black-Scholes model, more comparative pricing and precise risk management in equity options can be achieved by incorporating term-structures of interest rates, volatility and dividend into the CEV option valuation model.

Keywords: CEV option, similarity transformation, Bessel equation, moving barrier

JEL Classification: G13

Suggested Citation

Lo, Chi-Fai and Tang, Hoi-Man and Ku, K. C. and Hui, Cho-Hoi, Valuing Time-Dependent CEV Barrier Options (June 1, 2009). Journal of Applied Mathematics and Decision Sciences, pp. 1-17, 2009. Available at SSRN: https://ssrn.com/abstract=1113633

Chi-Fai Lo (Contact Author)

The Chinese University of Hong Kong ( email )

Department of Physics
Shatin, N.T., Hong Kong
China

Hoi-Man Tang

The Chinese University of Hong Kong (CUHK) ( email )

Hong Kong

K. C. Ku

The Chinese University of Hong Kong (CUHK) ( email )

Shatin, N.T.
Hong Kong
Hong Kong

Cho-Hoi Hui

Hong Kong Monetary Authority - Research Department ( email )

Hong Kong
China

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