Calibrating Distribution Models from PELVE (Q6583013)

The value at risk (VaR) and the expected shortfall (ES) are the two most popular risk measures in banking and insurance regulation. The value of probability equivalent level of VaR-ES (PELVE) is the multiplier to the tail probability when replacing VaR with ES such that the capital calculation stays unchanged. The authors study the problem of PELVE calibration -- how to find (from data or from expert opinion) a distribution model that yields a given PELVE and discuss separately the cases when one-point, two-point, \(n\)-point, and curve constraints are given. In the most complicated case of a curve constraint, the authors convert the calibration problem to that of an advanced differential equation.\N\NThe model calibration techniques are applied to estimation and simulation for datasets used in insurance. Also, some technical properties of PELVE are considered and a few new results on monotonicity and convergence are offered.