We present new evidence on disaggregated profit and loss (P/L) and value-at-risk (VaR) forecasts obtained from a large international commercial bank. Our data set includes the actual daily P/L generated by four separate business lines within the bank. All four business lines are involved in...

State-of-the-art stochastic volatility models generate a "volatility smirk" that explains why out-of-the-money index puts have high prices relative to the Black-Scholes benchmark. These models also adequately explain how the volatility smirk moves up and down in response to changes in risk....

Characterizing asset return dynamics using volatility models is an important part of empirical finance. The existing literature on GARCH models favors some rather complex volatility specifications whose relative performance is usually assessed through their likelihood based on a time series of...