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 solving the fixed point problem in closed form. We apply our results to stochastic volatility and option pricing.
Also included in AXA Working Paper Series No 2.