Keep on Smiling: Market Imbalance, Option Pricing, and the Volatility Smile

Abstract

The Black-Scholes model, which is widely used to price financial options, assumes that volatility is constant as a function of strike price. However when market option prices are used to infer the volatility that is implied by those prices, it often exhibits a marked dependence on strike price which is characterised by a smile or skew shape. This paper argues that the volatility smile is “real” in the sense that volatility and price change are correlated through the degree of market imbalance. We test a formula for the volatility smile, derived from a quantum oscillator model of stock markets, against historical market data. It is seen that the Black-Scholes model systematically misprices options, but that option pricing performance can be improved by taking the smile into account.

Keywords: financial options, implied volatility, stock markets, quantum economics, quantum finance

JEL Classification: G10, G12