Option pricing for infinite variance data

Abstract

Infinite variance distributions are among the competing models used to explain the non-normality of stock price changes (Mandelbrot, 1963; Fama, 1965; Mandelbrot and Taylor, 1967; Rachev and Samorodnitsky, 1993). We investigate the asymptotic option price formula in infinite variance setting for both independent and correlated data using point processes. As we shall see the application of point process models can also lead us to investigate a more general option price formula. We also apply a recursion technique to quantify various characteristics of the resulting formulas. It shows that such formulas, and even their approximations, may be difficult to apply in practice. A nonparametric bootstrap method is proposed as one alternative approach and its asymptotic consistency is established under a resampling scheme of m = o(n). Some empirical evidence is provided showing the method works in principle, although large sample sizes appear to be needed for accuracy. This method is also illustrated using publicly available financial data.