Measuring Value-at-Risk for Mortgage Backed Securities

Summary

This paper investigates the computation of Value-at-Risk (VaR) measures for mort-gage backed securities (MBSs) using data for the Danish MBS market. The current RiskMetrics proposal from J.P. Morgan is used as a reference point throughout, but the study diverges somewhat from their proposal, especially with respect to the estimation of zero coupon yield curves as well as in the choice of mapping techniques.

The MBS-valuation is done by a model developed in Jakobsen (1992,1994), which includes burn-out effects without the need for Monte Carlo simulation. The mapping of delta-equivalent cash flows uses the mapping technique proposed by Ho (1992). The resulting procedure can be employed even for large portfolios of MBS issues with the use of standard computing equipment.

The paper compares the MBS VaR estimates for a daily horizon to actual profits and losses for the period January 1993 to March 1995. The results seem to indicate that our method underestimates the variance of actual returns. However, as discussed in the paper this might be due to the fact that the correlation structure of zero coupon rates was estimated without any a priori restrictions. A study which uses the correlations provided in the RiskMetrics dataset might yield better results.

The author wishes to thank Bo Wase Petersen, Carsten Tanggaard and Thorns Øyvind for valuable help and comments. All computations have been done with software developed by Carsten Tanggaard and the author.