Value-at-Risk for fixed-income portfolios: a Kalman filtering approach

Abstract

We propose a way of measuring the risk of a sovereign debt portfolio by using a simple two-factor short rate model. The model is calibrated from data and then the changes in the bond prices are simulated by using a Kalman filter. The bond prices being simulated remain arbitrage-free, in contrast with principal component analysis-based strategies for simulation and risk measurement of debt portfolios. In liquid sovereign debt markets, a risk measurement methodology which allows the future bond price scenarios to be arbitrage-free may be seen as a potentially more realistic way of measuring the debt portfolio risk due to interest rate fluctuations. We demonstrate the performance of this methodology with calibration and backtesting, both on simulated data as well as on a real portfolio of US government bonds.