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. This paper was accepted by Wei Xiong, finance.
We develop an equilibrium model in a 2-country, 2-good, pure exchange economy in which investors with logarithmic utility functions have heterogeneous beliefs about exogenously given output or endowment processes. We obtain closed-form representations of real exchange rates and of stock prices. We show that heterogeneous beliefs together with heterogeneous preferences make the volatility of real exchange rates and of stocks exhibit some properties that have been well documented in the empirical literature. These properties include the high volatility of both real exchange rates and stocks compared with that of economic fundamentals, the high correlation of stocks during periods of volatile markets. The model can also generate the clustering of the volatility of foreign exchange rates and stocks if the differences of beliefs are clustering.
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