Parameter estimation and behavior in the Black-Scholes model

Abstract

This study uses nonlinear regression to estimate implied parameter values from the option pricing model and tests their theoretical behavior with standard parametric and nonparametric statistical techniques. The data employed are the Berkeley Options Data Base tapes which contain exactly coincident stock and option price quotations. The research intent is to focus on the limitations of existing option pricing models by observing the behavior of implied parameter values. The results suggest methodological improvements applicable to future research as well as directions to further explore in option price modeling. Statistical results show that there is a time dimension to implied stock return volatilities. In general, near-term options exhibit higher implicit stock return standard deviations than do options further from expiration. Future option pricing research should encompass this inverse proportionality of volatility and time to expiration. Results show the implicit "riskless" rate of return to be systematic and option expiration-independent, thereby supporting the concept of forming a riskless (hedged) stock/option portfolio. This result fosters a novel and more accurate method of estimating the riskfree rate of interest. The data show that the family of commercial paper rates best correlates with the riskfree return implicit in option pricing and should be the proxy used in future options research. Finally, the study demonstrates the superiority of transactions data over closing stock and option price quotations. Significantly different results occur when using closing versus coincident data. The immediate implication is that use of closing data in option pricing research should be minimized.