Asi se llama un reciente post del blog de Kamakura Corp. De forma inteligente parte de una noticia sobre BP, para elegantemente criticar -y hacer un poco de PR de su método alternativo- el conversor de CDS de ISDA de spread basis a upfront basis.
As Prof. Jarrow describes it, there are two ways to understand the linkages between CDS spreads and default probabilities:
Bottoms up approach: Build a model, assume it’s true, and solve for continuous default probability (“risk neutral”) that matches observable pricing
Top down approach: Determine the factors driving the intersection of supply and demand and use an econometric approach to derive (empirical) default probabilities
The ISDA Standard CDS Converter is a “bottoms up” approach that makes a number of simplifying assumptions, something very much in keeping with the “yield to maturity” analogy:
- Forward interest rates are step-wise constant, not a smooth continuous curve such as those we have discussed in our many blogs on yield curve smoothing
- Default intensity, the continuous time probability of default, is constant over the life of the credit default swap contract. Similarly, the yield to maturity formula assumes that interest rates are constant over the life of the bond in question.
- The only relevant factors to consider are the instantaneous probability of default, the recovery rate, and interest rate levels
- The counterparty on the CDS contract will not default
There is nothing wrong with this approach–as long as one is aware of its limitations. The yield to maturity formula, for example, is deeply embedded in bond markets but it is well known that it is not best practice for valuation or risk management. In the same way, the ISDA Standard CDS Converter is embedded in the mechanics of settlement but it is too simple for accurate valuation and risk management.
The reason the ISDA Standard CDS Converter is too simple is that it assumes only three factors affect the link between CDS spreads and default probabilities:
- Interest rates
- Recovery rates
- The constant continuous time default intensity
We now turn to the “top down” approach to show why the ISDA Standard CDS Converter is too simple for accurately describing the links between spreads and default probabilities. Instead of assuming the (ISDA) theory is true, we assume the market data is true and derive insights from it. In this section, we summarize our findings in the RISK 2007 publication and companion blog entry listed above. For data on default probabilities, we used the then-current reduced form or “Jarrow-Chava” default probabilities from Kamakura Risk Information Services.