This article develops a multi-factor econometric model of the term structure of interest-rate swap yields. The model accommodates the possibility of counterparty default, and any differences in the liquidities of the Treasury and Swap markets. By parameterizing a model of swap rates directly, we are able to compute model-based estimates of the defaultable zero-coupon bond rates implicit in the swap market without having to specify a priori the dependence of these rates on default hazard or recovery rates. The time series analysis of spreads between zero-coupon swap and treasury yields reveals that both credit and liquidity factors were important sources of variation in swap spreads over the past decade. ALTHOUGH PLAIN VANILLA FIXED-for-floating interest-rate swaps comprise a major segment of the fixed-income derivative market, notably few econometric models for pricing swaps have been developed in the literature. Perhaps the primary reasons for this are: (i) swap contracts embody default risk and hence equilibrium or arbitrage-free term structure models developed for default-free government bond markets are not directly applicable to the swap market; (ii) empirical modeling of the default event underlying credit spreads on defaultable bonds and swaps has met with limited success at explaining the timeseries properties of spreads; and (iii) swap spreads are likely to depend on other factors such as liquidity that are not directly related to default events. Also, until recently, data have not been widely available. In this article we develop a multifactor econometric model of the term structure of U.S. fixedfor-floating interest-rate swap yields that accommodates many of the institutional features of swap markets. Specifically, using results in Duffie and Singleton (1996), we show that the fixed payment rate of a swap, assuming that the floating rate is London Interbank Offering Rate (LIBOR), can be expressed in terms of present values of net cash flows of the swap contract

An Econometric Model of the Term Structure of Interest-Rate Swap Yields

The risk of default affects virtually every financial contract. Therefore the pricing of default risk has received much attention; both from traders, who have a strong interest in pricing transactions accurately, and from financial economists, who have much to learn from the way such risks are priced in markets. The standard theoretical paradigm for modeling credit risks is the contingent claims approach pioneered by Black and Scholes. Much of the literature follows Merton (1974) by explicitly linking the risk of a firm’s default to the variability in the firm’s asset value. Although this line of research has proven very useful in addressing the qualitatively important aspects of

/pdf/estimating-the-price-of-default-risk-wt2l98t9ng.pdf

Estimating the Price of Default Risk

This article presents a model for valuing claims subject to default by both contracting parties, such as swaps and forwards. With counterparties of different default risk, the promised cash flows of a swap are discounted by a switching discount rate that, at any given state and time, is equal to the discount rate of the counterparty for whom the swap is currently out of the money (that is, a liability). The impact of credit-risk asymmetry and of netting is presented through both theory and numerical examples, which include interest rate and currency swaps. THIS ARTICLE PRESENTS A model for valuing claims subject to default by both contracting parties, such as swaps and forwards. This extends the valuation model for defaultable claims proposed by Duffie and Singleton (1994) to cases in which the two counterparties have asymmetric default risk. The extension permits a reexamination 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 a floating rate such as the London Inter Bank Offered Rate (LIBOR) 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 article is to provide a simple and theoretically consistent model allowing such computations.

Swap Rates and Credit Quality

Counterparty credit risk has become one of the highest-profile risks facing participants in the financial markets. Despite this, relatively little is known about how counterparty credit risk is actually priced. We examine this issue using an extensive proprietary data set of contemporaneous CDS transaction prices and quotes by 14 different CDS dealers selling credit protection on the same underlying firm. This unique cross-sectional data set allows us to identify directly how dealers’ credit risk affects the prices of these controversial credit derivatives. We find that counterparty credit risk is priced in the CDS market. The magnitude of the effect, however, is vanishingly small and is consistent with a market structure in which participants require collateralization of swap liabilities by counterparties.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID2190086_code683384.pdf?abstractid=1830321&type=2

Counterparty Credit Risk and the Credit Default Swap Market

The book’s content is focused on rigorous and advanced quantitative methods for the pricing and hedging of counterparty credit and funding risk The new general theory that is required for this methodology is developed from scratch, leading to a consistent and comprehensive framework for counterparty credit and funding risk, inclusive of collateral, netting rules, possible debit valuation adjustments, re-hypothecation and closeout rules The book however also looks at quite practical problems, linking particular models to particular ‘concrete’ financial situations across asset classes, including interest rates, FX, commodities, equity, credit itself, and the emerging asset class of longevity

	The authors also aim to help quantitative analysts, traders, and anyone else needing to frame and price counterparty credit and funding risk, to develop a ‘feel’ for applying sophisticated mathematics and stochastic calculus to solve practical problems

	The main models are illustrated from theoretical formulation to final implementation with calibration to market data, always keeping in mind the concrete questions being dealt with The authors stress that each model is suited to different situations and products, pointing out that there does not exist a single model which is uniformly better than all the others, although the problems originated by counterparty credit and funding risk point in the direction of global valuation

	Finally, proposals for restructuring counterparty credit risk, ranging from contingent credit default swaps to margin lending, are considered

/pdf/counterparty-credit-risk-collateral-and-funding-with-pricing-43xk5tcc92.pdf

Counterparty Credit Risk, Collateral and Funding: With Pricing Cases For All Asset Classes

With the growth in the market for interest rate swaps has come a growing need to understand the potential default risks of these instruments. In general, swap participants can deal with default risk by seeking to mitigate it (by dealing only with AAA-rated counterparties, for example). Alternatively, potential counterparties can attempt to come to some agreement about the degree of default risk and use that knowledge to "price" their positions. A model of swap default risk evaluates jointly the probability of the swap counterparty defaulting and the cost (or impact) of the default for the solvent party. The model helps to establish the correct level for a swap between risky (or potentially risky) parties. The key considerations are the swap parties' credit conditions and the shape and volatility of the yield curve.

Thierry F. Bollier

Papers

Pricing Swap Default Risk