Heterogeneous Beliefs, Option Prices, and Volatility Smiles∗

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 implied volatility surface exhibits the observed patterns that are widely documented in various options markets. Furthermore, the prices of barrier options and hedging deltas can be approximated at any desired level of accuracy. In some cases, barrier and one-touch options 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 rational for the observed implied volatility patterns in an equilibrium setting but also is easy to use in practice. ∗Department of Finance, Faculty of Business Administration, the Chinese University of Hong Kong, Shatin, N.T., Hong Kong. Tel: +852 2609 7757, Fax: +852 2603 6586, E-mail: [email protected]. Heterogeneous Beliefs, Option Prices, and Volatility Smiles