Investors' Heterogeneity and Implied Volatility Smiles

Heterogeneity in beliefs and time preferences among investors make stock volatility stochastic, even though the volatility of the underlying dividend is constant. Prices of the European options written on this stock admit closed‐form solutions, hence their hedging deltas. The Black–Scholes implied volatility surface, which depends on wealth distribution, investors' beliefs, and time preferences, exhibits observed patterns that are widely documented in various options markets. Along with benchmark models, the model is calibrated weekly to the S&P 500 index options from January 1996 to April 2006. It shows comparable performance to the stochastic volatility and jump model and outperforms the traders' rules and two no‐arbitrage models (stochastic volatility, and stochastic volatility and stochastic interest rate) in terms of out‐of‐sample pricing errors.