Trade Simulation among Heterogeneous Agents: How the Risk Aversion Distribution Influences Volatility Implied by Option Prices

This work studies how heterogeneity in risk aversion among agents can fit financial data, with special focus on explaining the volatility of returns. The key feature of the model is to simulate option trade among agents who have different risk aversion coefficients. A dynamic portfolio choice problem between an option index using the Black-Scholes formula and a riskless asset yields a series of implied volatility. This implied volatility is fitted to realized volatility through searching for the risk-aversion distribution parameters. The solution method allows for using arbitrary utility functions, return distributions, short-selling, leverage constraints and a large number of state variables. We show that models with heterogeneity outperform homogeneous models, but yield smaller implied volatility within 5-years sample. Yearly data highlights that sensitivity of implied volatility to heterogeneity in risk aversion varies over time and tend to be positive. In the model, the mean and variance of risk aversion coefficients increase with the number of individuals allowed to trade. Additionally, the more heterogeneous in risk aversion agents are, the more volatile is the market. The model agrees with previous theoretical findings: over time wealth tends to be allocated among less risk averse traders; the model also yields volatility smiles that are more skewed for options, that are closer to maturity.