In this contribution it is demonstrated that XploRe can be used as a tool in the analysis of time series of market data and empirical loss distributions. The focus of this contribution is on the analysis of spread risk. Yield spreads are an indicator of an obligor's credit risk. The distributions of spread changes are leptokurtic with typical fat tails, which makes the application of conventional variance-covariance risk models problematic. That is why in this contribution we prefer the analysis of spread risk by means of historical simulation. Since it is not a priori clear, how spread risk should be integrated in a risk model for interest rate products and how it can be separated from general market risk, we investigate several possibilities, which include modelling the full yield curve (i.e., consideration of only one risk factor category, which covers both benchmark and spread risk) as well as separately modelling spread risk and benchmark risk. The aggregation of both risk categories is carried out in a conservative way (addition of the risk measure for both risk categories) as well as coherently (simultaneous simulation of spread and benchmark risk). Moreover, in addition to the basic historical simulation method we add additional features like mean adjustment and volatility updating. Risk is quantified by means of a quantile-based risk measure in this contribution - the VaR. We demonstrate the differences between the different methods by calculating the VaR for a fictive zero-bond.
The numerical results indicate, that the conservative approach over-estimates the risk of our fictive position, while the simulation results for the full yield as single risk factor are quite convincing. The best result, however, is delivered by a combination of simultaneous simulation of spread and benchmark risk and volatility updating, which compensates for non-stationarity in the risk factor time series. The conclusion from this contribution for model-builders in the banking community is, that it should be checked, whether the full yield curve or the simultaneous simulation with volatility updating yield satisfactory results for the portfolio considered.