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.

This paper presents a new heuristic for fast approximation of VaR (Value-at-Risk) and CVaR (conditional Value-at-Risk) for financial portfolios where the net worth of portfolio is a nonlinear function of possibly non-Gaussian risk factors. The proposed method is based on mapping non-normal marginal distributions into normal distributions via a probability conserving transformation and then using a quadratic, i.e. Delta-Gamma approximation for the portfolio value. The method is extremely general and can deal with a wide range of marginal distributions of risk factors, including non-parametric distributions. Its computational load is comparable with Delta-Gamma-Normal method based on Fourier inversion. However, unlike the Delta-Gamma-Normal method, the proposed heuristic preserves the tail behavior of the individual risk factors, which may be seen as a significant advantage. We demonstrate the utility of the new method with comprehensive numerical experiments on simulated as well as real financial data.