Consistent Spread Dynamics for CVA Risk Charge and Historical Value-at-Risk by Means of Cross Sectional / Consolidated Bucket Link Copula Simulation

Abstract

This paper describes the modelling of spread risk, in case of missing or illiquid market data, by using a subset of good quality liquid bond/credit default swap (CDS) spread time series. The proposed method links copula simulation to the actual historical spread dynamics. This is important when calculating credit valuation adjustment (CVA) risk charge and Value-at-Risk (VaR) with historical simulation. The methodology center around buckets of similar spreads. Buckets with good data, are straight forward, whereas buckets without data rely on a cross sectional model spread based on other buckets with good data. Residuals from regression of the bucket spread returns against market index returns are used to derive a link for each bucket. The link is subsequently used for simulating the spread dynamics in case of missing or illiquid spreads, using a modified one factor copula. A link between the actual and simulated residuals maintaining the risk dynamics is thus ensured. The result of the copula simulation is transformed into quantiles that are plugged into residual distributions from actual quality data, thereby maintaining the properties of actual market data such that the choice of copula only affects the risk dynamics, not the distributions of the risk factors.