A New Simple Square Root Option Pricing Model

摘要

This study derives a simple square root option pricing model using a general equilibrium approach in an economy where the representative agent has a generalized logarithmic utility function. Our option pricing formulae, like the Black-Scholes model, do not depend on the preference parameters of the utility function of the representative agent. Although the Black-Scholes model introduces limited liability in asset prices by assuming that the logarithm of the stock price has a normal distribution, our basic square root option pricing model introduces limited liability by assuming that the square root of the stock price has a normal distribution. The empirical tests on the S&P 500 index options market show that our model has smaller fitting errors than the Black-Scholes model, and that it generates volatility skews with similar shapes to those observed in the marketplace.