Hedging of Time Discrete Auto-Regressive Stochastic Volatility Options

Numerous empirical proofs indicate the adequacy of the time discrete auto-regressive stochastic volatility models introduced by Taylor (Taylor S. J. [1982]; Taylor S. J. [1986]; Taylor S. J. [2005]) in the dynamical description of the log-returns of financial assets. The pricing and hedging of contingent products that use these models for their underlying assets is a complicated task due to the incomplete nature of the corresponding market and the non-observability of the associated volatility process. In this paper we introduce new pricing kernels for this setup and apply two existing volatility filtering techniques available in the literature for these models, namely Kalman filtering and the hierarchical-likelihood approach, in order to implement various pricing and dynamical hedging strategies. An extensive empirical analysis using both historical returns and options data illustrates the advantages of this model when compared with more standard approaches, namely Black-Scholes and GARCH.