Option Risk Measurement With Time-Dependent Parameters

In value-at-risk (VaR) methodology of option risk measurement, the determination of market values of the current option positions under various market scenarios is critical. Under the full revaluation and factor sensitivity approach which are accepted by regulators, accurate revaluation and precise factor sensitivity calculation of options in response to significant moves in market variables are important for measuring option risks in terms of VaR figures. This paper provides a method for pricing equity options in the constant elasticity variance (CEV) model environment using the Lie-algebraic technique when the model parameters are time-dependent. Analytical solutions for option values incorporating time-dependent model parameters are obtained in various CEV processes. The numerical results, which are obtained by employing a very efficient computing algorithm similar to the one proposed by Schroder [11], indicate that the option values are sensitive to the time-dependent volatility term structures. It is also possible to generate further results using various functional forms for interest rate and dividend term structures. From the analytical option pricing formulae, one can achieve more accuracy to compute factor sensitivities using more realistic term-structures in volatility, interest rate and dividend yield. 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 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.