Backtesting the specific risk model is nontrivial as it is difficult to separate specific risk components from general market risk components in the changes of underlying risk factors. As described in the OSFI guidelines [8], debt specific risk is classified as risk arising from companyspecific factors and is composed of two components: credit event risk (rating migration) and default risk (credit default). Therefore, in estimating debt specific risk P/L, we need to capture the static P/L due to changes in credit risk factors with market risk parameters held constant over the day.
Under the proposed backtesting methodology, debt specific P/L is calculated as the difference between the total P/L and the gross general market risk P/L. Let Total PL(t +1,t ) - denote the actual P/L of a certain position from business day t (COBDate1) to the next business day t +1. According to the marking-to-market methodology, Total PL(t +1,t ) - is the difference in the mark-to-market (MTM) value of the position over the day.
It is worth to note that the gross general market P/L include the P/L impact of the changes in all underlying market factors including equity prices of the issuer. For regulatory purposes, the P/L impact of equity price changes is decomposed into two components: general equity P/L and specific equity P/L. The general equity P/L is determined from changes in the equity indices that are used in the regression model of each stock price.
The specific equity P/L is determined from the error of the predicted stock price (from the regression model and the equity indices) and the actual stock price change. Therefore, in the market risk parameters t M , if there is an equity risk parameter, we should use equity prices of the issuers, not the prices (see https://finpricing.com/lib/EqBarrier.html) of the equity index (or indices) into which the issuer is mapped. Otherwise, the debt specific risk P/L would have contained an equity specific risk component, which leads to an overestimate of DSR PL(t +1,t ).
Currently, there are two types of interest (zero) curves available for each currency: the base curve and the swap spread curve. The base curve can be understood as the curve against which interest rate risk hedges are performed. For USD/CAD, the government curve is defined as the base curve because government issued instruments are generally used to hedge interest rate sensitive positions. For all other currencies, the swap curve is defined as the base curve because swaps are generally used for hedging purposes (due to the lack of liquidity of the government issues).
Swap spread curve is the difference between the swap curve and government curve. Swap spread curves for all currencies are physically stored in the database but they are defined differently for different currencies. For USD/CAD, the swap spread curve is defined as swap curve minus the government curve (the base curve) and is generally positive. For all other currencies, the swap spread curve is defined as government curve minus swap curve (the base curve) and is generally negative.