Bayesian Lower and Upper Estimates for Ether Option Prices with Conditional Heteroscedasticity and Model Uncertainty

Abstract

This paper aims to leverage Bayesian nonlinear expectations to construct Bayesian lower and upper estimates for prices of Ether options, that is, options written on Ethereum, with conditional heteroscedasticity and model uncertainty. Specifically, a discrete-time generalized conditional autoregressive heteroscedastic (GARCH) model is used to incorporate conditional heteroscedasticity in the logarithmic returns of Ethereum, and Bayesian nonlinear expectations are adopted to introduce model uncertainty, or ambiguity, about the conditional mean and volatility of the logarithmic returns of Ethereum. Extended Girsanov’s principle is employed to change probability measures for introducing a family of alternative GARCH models and their risk-neutral counterparts. The Bayesian credible intervals for “uncertain” drift and volatility parameters obtained from conjugate priors and residuals obtained from the estimated GARCH model are used to construct Bayesian superlinear and sublinear expectations giving the Bayesian lower and upper estimates for the price of an Ether option, respectively. Empirical and simulation studies are provided using real data on Ethereum in AUD. Comparisons with a model incorporating conditional heteroscedasticity only and a model capturing ambiguity only are presented.