Journal of Applied Mathematics and Decision Sciences
Volume 2009 (2009), Article ID 359623, 17 pages
Research Article

Valuing Time-Dependent CEV Barrier Options

1Institute of Theoretical Physics and Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
2Research Department, Hong Kong Monetary Authority, 55th Floor, Two International Finance Centre, 8 Finance Street, Hong Kong

Received 15 January 2009; Accepted 29 May 2009

Academic Editor: Henry Schellhorn

Copyright © 2009 C. F. Lo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 multistage 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.