Integral Time Counter Simulations of GARCH for Option Pricing

Authors- Bitakwate Jackila Eliot

Abstract-This paper displays derivation of the univariate and multivariate GARCH(1,1) model. The Stochastic Discount Factor and conditional Esscher transform were used as techniques to de- rive the models. The matrix discretized form of the multivariate equation is also displayed in this paper with a proposed error correction in the normalized and variance matrices. Standard as- sumptions on the parameter were critically assigned and set to ensure convergences and stability for the models. The simulations in the risk-neutral processes shown approximate values as Mont Carlo simulations in Duan (2000) with values of the standard deviation ranging from [0.0999 , 0.5623] and payoff European call options [0.0000, 1.1692]. Using python and R programming tools, simulations showed that the risk neutral processes and the multivariate GARCH(1,1) can be used to predict returns and even price derivatives.

DOI: /10.61463/ijset.vol.12.issue5.294