The burgeoning market for sovereign credit default swaps (CDS) contracts offers a nearly unique window for viewing investors’ risk-neutral probabilities of major credit events impinging on sovereign issuers, and their risk-neutral losses of principal in the event of a restructuring or repudiation of external debts. In contrast to many “emerging market” sovereign bonds, sovereign CDS contracts are designed without complex guarantees or embedded options. Trading activity in the CDS contracts of several sovereign issuers has developed to the point that they are more liquid than many of the underlying bonds.
Moreover, in contrast to the corporate CDS market, where trading has been concentrated largely in the five-year maturity contract, there are actively traded CDS contracts at several maturity points between one and ten years. As such, a full term structure of CDS spreads is available for inferring default and recovery information from market data.
This paper explores in depth the nature of the risk-neutral credit-event intensities (?Q) that best describe the term structures of sovereign CDS spreads. Since little is known about the nature of the market-implied ?Q processes that underlie the term structures of survival probabilities for sovereign issuers, we examine three distinct families of stochastic processes: the square-root (Cox, Ingersoll, and Ross [1985]), lognormal, and three-halves (Ahn and Gao [1999]). While all three models allow for mean reversion in ?Q, they differ in the degree of nonlinearity in their drifts. They also differ in their assumptions about the dependence of the instantaneous volatilities of ?Q on itself: they take the form (?Q)?, with ? equal to .5 (square-root), 1 (lognormal), or 1.5 (three-halves).
Equally central to modeling the credit risk of sovereign issuers is the recovery in the event of default. Standard practice in modeling corporate CDS spreads is to assume a fixed risk-neutral loss rate LQ, largely because the focus has been on the liquid five-year CDS contract.1 We depart from this literature and exploit the term structure of CDS spreads to separately identify both LQ and the parameters of the process ?Q. That we even attempt to separately identify these parameters of the default process may seem surprising in the light of the apparent demonstrations in Duffie and Singleton [1997], Houweling and Vorst [2003], and elsewhere of the infeasibility of achieving this objective. We show that in fact, in market environments where recovery is a fraction of market value, as is the case with CDS markets, these parameters are separately identified, at least over the relevant region of the admissible parameter space.
The maximum likelihood (ML) estimates of the parameters imply that the Q-distribution of ?Q shows very little mean reversion and, in fact, ?Q is explosive for several countries and models. The lower the estimate of the risk-neutral loss rate LQ, the greater the tendency for ?Q to follow a Q-explosive process. This interplay between the loss rate and the persistence in ?Q is intuitive in that both a higher value of LQ and a more explosive ?Q are associated with more adverse default environments for risk-neutral investors. Under the measure associated with the historical data-generating process, ?Q shows substantial mean reversion, consistent with the autocorrelation properties of CDS spreads.
Download
PDF Ebook Default and Recovery Implicit in the Term Structure of Sovereign CDS Spreads
