Option Pricing for Infinite Variance Data

    • Ishwaran, H., Jahandideh, M. T., Zarepour, M.,   (2008)  Option Pricing for Infinite Variance Data. Published in  Statistics Vol. 42-3, Pages 245-260.

We consider the asymptotic option pricing formula under an infinite variance paradigm using a randomized version of the Cox-Ross-Rubinstein binomial option pricing-approach. We discuss practical difficulties in applying the asymptotic formula and suggest a non-parametric bootstrap as an estimation technique. Using point process theory, the asymptotic consistency of the bootstrap approach is established under a resampling scheme of m=o(n). We briefly discuss extension to correlated data and show that option pricing formula may no longer be valid in such settings. Finally, we consider a finite variance setting involving innovations from a variance gamma process. We derive the asymptotic option pricing formula and show that the non-parametric bootstrap is consistent.