Estimation of Risk Neutral Measures using the Generalized Two-Factor Log-Stable Option Pricing Model

We construct a simple representative agent model to provide a theoretical framework for the logstable option pricing model. We also implement a new parametric method for estimating the risk neutral measure (RNM) using a generalized two-factor log-stable option pricing model. Under the generalized two-factor log-stable uncertainty assumption, the RNM for the log of price is a convolution of two exponentially tilted stable distributions. Since the RNM for generalized two-factor log-stable uncertainty is expressed in terms of its Fourier Transform, we introduce a simple extension of the Fast Fourier Transform inversion procedure in order to reduce computational errors in option pricing. The generalized two-factor log-stable RNM has a very flexible parametric form for approximating other probability distributions. Thus, this model provides a sufficiently accurate tool for estimating the RNM from the observed option prices even if the log-stable assumption might not be satisfied. We estimate the RNM for the S&P 500 index options and find that the generalized two-factor log-stable model gives better performance than the Black-Scholes model, the finite moment log-stable model (Carr and Wu, 2003), and the orthogonal log-stable model (McCulloch, 2003) in fitting the observed option prices. † Economics Department, The Ohio State University, 1945 N. High St., Columbus OH 43210. Tel.: +1614-292-2070, E-mail address: [email protected] (S.H. Lee). The authors thank P. Evans, P.S. Lam, and R. Kimmel, and participants of the 2007 International Conference on Computing in Economics and Finance for helpful suggestions. JEL Field: C13, D81, G13. Keyword: Risk-neutral measure, option pricing, pricing kernel, stable distribution, exponentially tilted distribution, FFT.