Ebook Swap Rates and Credit Quality
This paper presents a model for valuing claims subject to default by both contracting parties. This extends the valuation model for defaultable claims proposed by Duffie and Singleton (1994) to cases in which the two counter parties have asymmetric default risk.
The extension permits a re-examination of the impact of credit risk on swap rates. While the valuation model applies to all forms of contingent claims in which both contracting parties are at risk to default, such as forward contracts, we focus on swaps for purposes of illustration.
For example, consider a 5-year interest rate swap between a given party paying floating LIBOR rates and another counterparty paying a fixed rate. Replacing the given fixed rate counterparty with a “lower-quality” counterparty whose bond yields are 100 basis points higher increases the swap rate by roughly 1 basis point, using our model and typical parameters for LIBOR rate processes.
This credit impact on swap rates is approximately linear within the range of normally encountered credit quality. For a 5-year currency swap, given a foreign exchange rate with 15 percent volatility, our model shows the impact of credit risk asymmetry on the market swap rate to be roughly 10-fold greater than that for interest rate swaps, that is, approximately 10 basis points in swap rate per 100 basis points in bond yield credit spread. The main goal of this paper is to provide a simple and theoretically consistent model allowing such computations.
The basic idea behind our model is that the impact of credit risk on swap rates depends on the probability distribution of the path taken by the value of the swap itself. When the swap value is positive for a given counterparty, it is the default characteristics (default hazard rate and fractional loss given default) of the other counterparty that are relevant for the backward recursive computation of the current swap value given its value at the next point in time.
The basic idea for this recursion was developed by Rendleman (1992). Rendleman’s model, however, is based on the impact of the swap value on the balance sheets of the counterparties, and considers the direct implications for structural insolvency (liabilities exceed assets). In order to address the problem of determining market swap rates, for which one cannot normally analyse the financial statements of the counterparties on a case-by-case basis with any degree of ease or accuracy, we develop a reduced-form model in which the default characteristics of the counterparties are directly estimated in terms of credit spreads.
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