VarGamma Stress Tests

Kent Osband

Volume 11, Number 2, Second Quarter 2013

Standard financial stress tests are ad hoc. They offer no guidance on how to select the target stress levels, how to adjust for randomness within crisis, or how to integrate the results with other risk measures. The VarGamma metric introduced by Osband (2013) offers an appealing alternative. It estimates a risk premium for crisis stress that can be added directly to the premium for ordinary risk. The use of cumulant generating functions for convolutions of variance-gamma distributions makes this analytically tractable. However, the general formula depends on unfamiliar parameters for the variance of extra crisis variance and the impact of variance on returns. This paper reformulates VarGamma crisis estimates using two more familiar parameters: the probability of crisis and the mean extra loss in crisis. The modeling assumptions are consistent with fat-tailed historical returns and near-ubiquitous option smiles. This opens new vistas for estimating fair market-implied risk premia at various levels of risk aversion.