Option pricing revisited: The role of price volatility and dynamics

Abstract

The analysis of option pricing in derivative markets has commonly relied on the Black-Scholes model. This paper presents a conceptual and empirical analysis of option pricing with a focus on the validity of key assumptions embedded in the Black-Scholes model. Going beyond questioning the lognormality assumption, we investigate the role played by two assumptions made about the nature of price dynamics: quantile-specific departures from a unit root process, and the role of quantile-specific drift. Our analysis relies on a Quantile Autoregression (QAR) model that provides a flexible representation of the price distribution and its dynamics. Applied to the soybean futures market, we examine the validity of assumptions made in the Black-Scholes model along with their implications for option pricing. We document that price dynamics involve different responses in the tails of the distribution: overreaction and local instability in the upper tail, and underreaction in the lower tail. Investigating the implications of our QAR analysis for option pricing, we find that failing to capture local instability in the upper tail is more serious than failing to capture “fat tails” in the price distribution. We also find that the most serious problem with the Black-Scholes model arises in its representation of price dynamics in the lower tail.