Volatility Smile in Option Prices May Reflect Heterogeneous Expectations: Theory and Empirical Evidence

If the underlying asset price process is unknown, arbitrageurs may not have sufficient incentive and confidence to use the underlying asset to arbitrage options. The option market makers can hedge their portfolios of temporary option inventories without the underlying asset, but investors’ risk attitudes and heterogeneous expectations could become relevant to option pricing. This paper shows that, if the investors just assume the lognormal process for the underlying asset price, but are heterogeneous on the drift and volatility, there exists an arbitrage-free option pricing function, providing that all the investors are risk-averse and the underlying asset is not involved. Since this pricing function allows the option market makers to achieve delta-neutrality and gamma-neutrality with their portfolios of options, the option market equilibrium is sustainable. This option pricing model implies that the risk-neutral probability distribution is a finite mixture of lognormal distributions, which can be easily recovered from observed contemporaneous options quotes by a parametric method. The empirical results support the model.