Banks operating under Value-at-Risk constraints give rise to a welldefined aggregate balance sheet capacity for the banking sector as a whole that depends on total bank capital. Equilibrium risk and market risk premiums can be solved in closed form as functions of aggregate bank capital. We...

Market volatility reflects traders' actions, while their actions depend on perceptions of risk. Equilibrium volatility is the fixed point of the mapping that takes perceived risk to actual risk. We solve for equilibrium stochastic volatility in a dynamic setting where risk-neutral traders...

Risk management systems in current use treat the statistical relations governing asset returns as being exogenous, and attempt to estimate risk only by reference to historical data. These systems fail to take into account the feedback effect in which trading decisions impinge on prices. We...

Banks operating under Value-at-Risk constraints give rise to a well-defined aggregate balance sheet capacity for the banking sector as a whole that depends on total bank capital. Equilibrium risk and market risk premiums can be solved in closed form as functions of aggregate bank capital. We...

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....

Risk management systems in current use treat the statistical relations governing asset returns as being exogenous, and attempt to estimate risk only by reference to historical data. These systems fail to take into account the feedback effect in which trading decisions impinge on prices. We...

Most financial risk regulations assume that asset returns are exogenous, where risk is estimated from historical data. This assumption fails to take into account the feedback effect of trading decisions on prices. We investigate the consequences of risk constrained trading by means of...

Banks operating under Value-at-Risk constraints give rise to a welldefined aggregate balance sheet capacity for the banking sector as a whole that depends on total bank capital. Equilibrium risk and market risk premiums can be solved in closed form as functions of aggregate bank capital. We...

Many financial applications, such as risk analysis and derivatives pricing, depend on time scaling of risk. A common method for this purpose, though only correct when returns are iid normal, is the square-root-of-time rule where an estimated quantile of a return distribution is scaled to a lower...