Heterogeneous Beliefs, Option Prices, and Volatility Smiles

Abstract

In an economy in which investors with different time preferences have heterogeneous beliefs about a dividend’s mean growth rate, the volatility of the stock that claims the dividend is stochastic in equilibrium. The prices of the vanilla European options that are written on this stock admit closed-form solutions, hence their hedging deltas. The Black-Scholes implied volatility surface exhibits the observed patterns that are widely documented in various options markets and depends on the wealth distribution, investors’ beliefs, and subjective discount rates. In addition, the prices of barrier options and hedging deltas can be approximated at any desired level of accuracy. In some cases, barrier and one-touch option prices and their hedging deltas can be closely bounded by closed-form formulae. In summary, the options pricing model that is developed in this paper not only offers a rationale for the observed implied volatility patterns in an equilibrium setting but also is easy to use in practice.