Deterministic versus stochastic volatility: implications for option pricing models

Abstract

The Black-Scholes (1973) option pricing model (BSOPM) rests on the assumption that the variance of stock returns is deterministic. However, if stock return volatility is a stochastic process, then the present form of commonly used option pricing models is misspecified and arbitrage-based arguments are invalid. The purpose of this paper is to investigate whether implied stock return volatility is deterministic (with non-linear dependencies) or stochastic. Correlation dimensions are computed using the method of Grassberger and Procaccia (1983) and simple bootstrapping techniques are applied in order to distinguish stochastic from deterministic systems. Results reported herein add support to the growing literature on preference-based stochastic volatility models and generally reject the notion of deterministic volatility.