A Lévy process for the GNIG probability law with 2nd order stochastic volatility and applications to option pricing

摘要

Here we derive the Lévy characteristic triplet for the GNIGprobability law. This characterizes the corresponding Lévyprocess. In addition we derive equivalent martingale measures withwhich to price simple put and call options. This is done under twodifferent equivalent martingale measures. We also present amultivariate Lévy process where the marginal probabilitydistribution follows a GNIG Lévy process. The main contributionis, however, a stochastic process which is characterized byautocorrelation in moments equal and higher than two, here amultivariate specification is provided as well. The main tool forachieving this is to add an integrated Feller square root process tothe dynamics of the second moment in a time-deformed Browninanmotion. Applications to option pricing are also considered, and abrief discussion is held on the topic of estimation of the suggestedprocess.