Risk Appetite and Endogenous Risk

Abstract

Risk is endogenous. Equilibrium risk is the fixed point of the mapping that takes perceived risk to actual risk. When risk-neutral traders operate under Value-at-Risk constraints, market conditions exhibit signs of fluctuating risk appetite and amplification of shocks through feedback effects. Correlations in returns emerge even when underlying fundamental shocks are independent. We derive a closed-form solution of equilibrium returns, correlation and volatility by solv-ing the fixed point problem in closed form. We apply our results to stochastic volatility and option pricing.