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.