VaR Optimisation and Regression Sensitivities

Abstract

Infinitesimal sensitivities, computed as derivatives of pricing functions, are useful to find high-frequency hedge ratios. However, they are less useful for the purpose of optimising 2-week VaR, especially if one includes shocks from stressed periods, as is required for applications to margin requirements for bilateral portfolios.

We compute regression sensitivities by using Krylov regularisation and find that they have a better quality P&L explain than ifinitesimal sensitivities. RniVaR (Risk- not-in-VaR) is define as the upper bound on errors in the sensitivities expansion. We suggest that RniVaR should be an add-on for SBA VaR (Sensitivities-Based-Approach VaR). We find that RniVaR is about 20% for unoptimised portfolios but can be as large as VaR itself for delta-neutral, optimised portfolios where the SBA approach breaks down.

We conclude that a full revaluation VaR is preferable for optimisation purposes over SBA VaR and that regression sensitivities are useful to fnd optimal hedge ratios.

Keywords: value-at-risk, sensitivities, derivatives, bilateral, margin, risk

JEL Classification: G13