Heterogeneous Beliefs, Option Prices, and Volatility Smiles

51 Pages Posted: 12 Jun 2006 Last revised: 25 Oct 2018

See all articles by Tao Li

Tao Li

City University of Hong Kong (CityUHK) - Department of Economics & Finance

Date Written: September 5, 2008


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. The model is calibrated to S&P 500 index options daily from 1996 to 2006. The model fits the data pretty well and outperforms trader rules in the terms of out-of-sample valuation errors.

A version of the model with learning, Investors' Heterogeneity and Implied Volatility Smiles, is available HERE

Keywords: Option Pricing, Barrier Options, Volatlity Smile, Heterogeneous Beliefs, Equilibrium Model

JEL Classification: G12, G13, D51, D58, E44

Suggested Citation

Li, Tao, Heterogeneous Beliefs, Option Prices, and Volatility Smiles (September 5, 2008). Available at SSRN: https://ssrn.com/abstract=890277 or http://dx.doi.org/10.2139/ssrn.890277

Tao Li (Contact Author)

City University of Hong Kong (CityUHK) - Department of Economics & Finance ( email )

83 Tat Chee Avenue
Hong Kong

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