An Empirical-Distribution-Based Option Pricing Model: A Solution to the Volatility Smile Puzzle

Abstract

The volatility smile that is generated by the Black-Scholes model has been traditionally attributed to an inappropriately assumed return distribution. Previous studies use alternative specifications such as stochastic volatility and jump diffusion models. However, these specifications do not eliminate the smile. Moreover, as documented by Das and Sundaram (1999), the return distributions that are generated by stochastic volatility and jump diffusion models do not match important characteristics of realized returns. We construct an alternative valuation procedure to price S&P 500 call options, using a histogram from past S&P 500 index daily returns. We find that the implied volatilities that are generated by our model do not exhibit substantial relationship to moneyness levels. Consistent with the absence of the smile, payoffs to holding options are also not related to moneyness levels. We also find that these payoffs are more closely related to our implied volatility measures than to the Black Scholes implied volatility measures. These findings indicate that our model is more appropriate than the Black-Scholes model to value S&P 500 call options.

Keywords: options, implied volatility, volatility smile, nonparametric model

JEL Classification: G12, G13