A Fast Algorithm to Combine Binomial Option Pricing Framework with Stochastic Volatility Forecasts from a T-GARCH Model for Valuation of Path Dependent Options : A Path Integral Approach

This article proposes a simple and intuitive framework to combine a discrete volatility forecast series produced by a GARCH model with the binomial tree methodology to price path-dependent options. The framework exploits the premise of the path integral methodology of combining the terminal states of a time-evolved Gaussian process with a positive potential function derived from the option pay-off and investigates a two-step backward bootstrapping procedure to construct re-combining binomial trees that capture the distributional properties of the volatility forecasts. Finally, the framework is employed to price European Asian options and the results are compared with prices obtained from counter-parties constituting major Wall Street banks and Bloomberg options calculator. The results look very promising, making a compelling case for the methodology proposed in this article to be researched further to extend it to pricing other financial contingent claims with path-dependent pay-offs