Default and Recovery Implicit in the Term Structure of Sovereign CDS Spreads -- Jun Pan and Kenneth J. Singleton (Oct., 2008)

Xue (Cindy) Hu9/26/2013

Agenda

IntroductionI. The Structure of Sovereign CDS

MarketII. Pricing Sovereign CDS ContractsIII. Separately Identify L Q and λQ

IV. The Maximum Likelihood (ML) Estimates of λQ

V. Priced Risks in Sovereign CDS Markets

Introduction• Definition• Settlement

• Physical delivery of an admissible bond• Term sheets:

• Obligation acceleration; failure to pay; restructuring; repudiation/moratorium

Figure: wiki

Example:

Source: Bloomberg

CDS on corporate bonds◦ Recall John Paulson and Michael Burry

European sovereign debt crisis◦ A combination of factors

December 1, 2011 the European Parliament has banned naked CDS on sovereign debts.

Debate in reconstruction of Greek Sovereign debt – trigger CDS payments

Countries that we will study: Korea, Turkey, and Mexico

Banks and Corporate

CDS

Earl 1990s

2002-2008 2007-2012 2008-2012

Easy Credit: Risk

Lending

Global Financial

Crisis

Global Recession

Example:

Source: Bloomberg

Compare liquidity of CDS market and bond market◦ Lower volume ◦ Higher liquidity for bonds with a boarder range of maturities

CDS spreads versus bond spreads • Darrell Duffie and Jun Liu 2001, Duffie and Singleton 2003;

I. The Structure of Sovereign CDS Market

Sample Periods for the paper:◦ March 19, 2001 through August 10, 2006.

Korea, Turkey, and Mexico◦ Geographically dispersed

Latin American, Eastern Europe, and Asia◦ A broad range of credit quality

Ratings of the three countries throughout the sample periods

◦ Regional representative◦ Relative liquidity

Liquidity of the cash market and CDS market◦ Compare CDS prices across different countries◦ Compare CDS prices across different maturities◦ Compare CDS bid-ask spreads across different countries◦ Compare CDS bid-ask spreads across different maturities

(Continued)

(Continued)

(Continued)

Figure 2. CDS Spreads: Mexico (upper), Turkey (left), and Korea (right), mid-market quotes.

(Continued)

Co-movement:◦ Co-movement of 1, 3, 5, and 10 years CDS

Principal component analysis:◦ First PC explains over 96% of the variation for all three

countries except 1-year Mexico CDS (90%)◦ Motivation for using one-factor model (Later in IV.B)

Persistent upward sloping trend◦ Mexico: the spread between 1 and 5 year is 112 bps on

average◦ Turkey: 5- and 1-year CDS spreads were -250 basis points

on March 29, 2001, -150 basis points on July 10, 2002, and -200 basis points on March 24, 2003.

◦ Why is the negative spread for Turkey? Domestic election Fall of Cyprus

(Continued)

II. Pricing Sovereign CDS Contracts

At issue, a CDS contract with semi-annual premium payments is priced as (see, e.g., Duffie and Singleton (2003)):

Recall the ISDA term sheet and the four types of credit events:

L Q and λQ

Now we have the arrival rate, what is the L Q ?I. Set L Q = .75II. Recoveries estimated by agencies

I. For example, Moody's (2003) estimates of the recoveries (weighted by issues sizes) on several recent sovereign defaults are: Argentina 28%, Ecuador 45%, Moldova 65%, Pakistan 48%, and Ukraine 69%.

II. Set L Q = L Q ?

III. At practical level:I. Set L = .75 and bootstrap λQ or use a one-factor

parametric model for the λQ process to match a day’s cross-section of spreads

Question: ◦ Can L Q and the conditional Q distribution of λQ be

separately identified from a time-series of market-provided spreads on newly issued CDS contracts?

III. Separately Identify L Q and λQ

Fractional recovery of market value convention (RMV) introduced by Duffie and Singleton (1999), with fixed y = L

Q X λQ

Fractional recovery of face value (RFV) (see Duffie (1998) and Duffie and Singleton (1999))

• The spreads clearly depend on LQ and their sensitivity to changes in L Q differs across maturities.

• This is to be contrasted against the RMV pricing framework in equation (7), un der which the sensitivity of a defaultable bond to variation in L Q is zero with fixed y = L Q X λQ

(Continued)

• Econometric identification may be sensitive to the choice of parameter values:• Fixing L= .75, price is sensitive to the volatility and mean

reversion.

(Continued)

Monte Carlo to simulate L

Q Monte Carlo and Maximum Likelihood (simulate 100

times)◦ Simulate affine model for 1, 3, 5, and 10 year CDS spreads◦ Then, add normally distributed errors◦ Use the resulting CDS to construct maximum likelihood

estimates of the underlying parameters

IV. The Maximum Likelihood (ML) Estimates of λQ

Approach I: Fixed L Q of .75 by market convention◦ An extensive Monte Carlo analysis of the small-sample

distributions of various moments reveals that many features of the implied distributions of CDS spreads for Mexico and Turkey are similar across the cases of L Q equal to 0.75 or 0.25.

◦ For our model formulation and sample ML estimates, it is only over long horizons - for most of our countries, longer than our sample periods - that the differences in P-mean reversion in the two cases manifest themselves.

Approach II: L Q as a free parameter◦ The likelihood functions call for much smaller values of L Q for

Mexico and Turkey, more in the region of 0.25, and also slower rates of P-mean reversion of λQ.

◦ For Korea, unconstrained estimates of L Q is close to .75.Therefore, set L Q = .75 for the rest of te study.

(Continued)• Kappa is negative under Q measure and positive under P

measure• For the unconstrained case, LQ is very low for Mexico and Turkey,

but LQ of Korea is close to the market convention

(Continued)• Recall last slide where κ PC > κPU, we expected larger

differences between autocorrelation of constrained cases be higher

• But the result shows that the difference is negligible

Pricing Errors Assumption: Single risk factor underlies for λQ

◦ Motivation: co-movement◦ PC1 explains a large variation of in spreads

Potential role of a second risk factor (particularly for shorter maturities)

Behaviors of bid-ask spreads. Is one-factor model enough? Among the various maturities, the one-factor model

misprices the 1-year con tract most severely.◦ Large institutes use 1 year CDS as their main

vehicle to sovereign exposure.

• The one-factor models match the correlations of levels of CDS spreads and slopes quite closely. The models do less well at matching the correlations among the first differences of these variables.

Take the ML estimates obtained in Section IV and construct two measures of fitted CDS spreads.

To quantify the role of risk premiums regarding variation in λQ in percentage terms, compute:

Watch out the peaks (run-up) of CRPt(M):

V. Priced Risks in Sovereign CDS Markets

(continued)

Observations-The adjustments to Mexico's risk premiums had the largest percentage effects on spreads

-Early 2003: Korea’s credit card issues; SK

-May 2004 : change in investors’ appetite for exposure to credit

-March 2005: GM & Ford

- 2006: large sell-off in EM equity market and unwinding carry trade in EM currencies; Turkey’s uncertainty of EU accession

(continued)

A formal analysis of 1) correlation between spreads and VIX,

2) the spreads between 10-year U.S. BB industrial corporate bonds and 6-month U.S. T-bill, and

3) the volatility in the own-currency options market

Results:◦ CDS premiums is influenced by spillovers of real

economic growth in the U.S. to other countries◦ Investors' appetites for credit exposure at a global level

outweighs the reassessments of the fundamental strengths of these specific sovereign economies

Summary A single-factor model with λQ following a lognormal

distribution captures the most variation of the term structure of CDS spreads.

Premiums on sovereign CDS:◦ Real economic growth of U.S. ◦ Change in investor’s appetites for credit exposure at a

global level

Looking ahead…◦ a joint analysis of CDS spreads and other credit-sensitive

derivative products. ◦ Case of Portugal CDS spreads

Source: Bloomberg

Sources Default and Recovery Implicit in the Term Structure of Sovereign CDS Spreads. Author(s): Jun Pan and Kenneth J. Singleton. Source: The Journal of Finance, Vol. 63, No. 5 (Oct., 2008), pp. 2345-2384Published by: Wiley for the American Finance Association Stable URL: http://www.jstor.org/stable/25094509. Accessed: 17/09/2013 14:50

Bloomberg

Thank you