Malkhaz Shashiashvili, professor of Ivane Javakhishvili Tbilisi State University (TSU) visited ISET on Thursday, September 17th to present his recent paper "Discrete Time Hedging of the American Option" co-authored with S. Hussain, professor of Government College University. Since his talk contained very complicated mathematical methods, Prof. Shashiashvili started the presentation with giving definitions and key words, in order to make it accessible for a general audience.
In contrast to widespread opinion –the best hedging options require the option’s writer to trade continuously in time. Prof. Shashiashvili claimed that it is possible to construct the perfect portfolio for a discrete amount of time. The perfect hedging requires the knowledge of the partial derivative of the value function of the American option in the underlying asset, which is not explicitly known in most cases of practical importance.
Having at hand any uniform approximation of the American option value function at equidistant discrete rebalancing times it is possible to construct a discrete time hedging portfolio, the value process of which uniformly approximates the value process of the continuous time perfect delta-hedging portfolio. Prof. Shashiashvili found a new type square integral estimate for the derivative of an arbitrary convex function and made it possible to estimate the discrete time hedging error for a perfect portfolio.
This was the first seminar for TSU Lecture Series for this fall semester and ISET would like to thank Prof. Shashiashvili for his insightful contributions to our students and faculty.