Option Pricing Under Autoregressive Random Variance Models

The autoregressive random variance (ARV) model introduced by Taylor (1980, 1982, 1986) is a popular version of stochastic volatility (SV) models and a discrete-time simplification of the continuous-time diffusion SV models. This paper introduces a valuation model for options under a discrete-time ARV model with general stock and volatility innovations. It employs the discretetime version of the Esscher transform to determine an equivalent martingale measure under an incomplete market. Various parametric cases of the ARV models, are considered, namely, the log-normal ARV models, the jump-type Poisson ARV models, and the gamma ARV models, and more explicit pricing formulas of a European call option under these parametric cases are provided. A Monte Carlo experiment for some parametric cases is also conducted.