Valuing Time-Dependent CEV Barrier Options

摘要

We have derived the analytical kernels of the pricing formulae of theCEV knockout options with time-dependent parameters for a parametric class of movingbarriers. By a series of similarity transformations and changing variables, we areable to reduce the pricing equation to one which is reducible to the Bessel equationwith constant parameters. These results enable us to develop a simple and efficientmethod for computing accurate estimates of the CEV single-barrier option prices aswell 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 forthe exact barrier option prices can be efficiently improved in a systematic manner. Itis also natural that this new approach can be easily applied to capture the valuationof other standard CEV options with specified moving knockout barriers. In view ofthe CEV model being empirically considered to be a better candidate in equity optionpricing than the traditional Black-Scholes model, more comparative pricing and preciserisk management in equity options can be achieved by incorporating term structuresof interest rates, volatility, and dividend into the CEV option valuation model.