Sovereign Credit Risk Analysis
through Statistical Modeling
Yoko Tanokura
Meiji University
November 28, 2013
International Conference on Mathematical Modeling and Applications 2013
Meiji University
This is the joint work withHiroshi Tsuda(Doshisha Univ.), Seisho Sato(Univ. of Tokyo) and Genshiro Kitagawa(ROIS)

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Measuring sovereign credit risk

Sovereign Credit Default Swap (SovCDS)...is an insurance contract that protects the buyer against the issuer’s credit riskof the country’s debt.
CDSbuyermake a payment on the occurrence of the credit event
periodically pay a CDS spread quoted as annual rate

CDSseller...can be regarded as the market evaluation on the credit risk for the country’s
economy.
Strictly speaking, although CDS spreads may include other factors such as risk premiums caused by its
fluctuations, it is not easy to extract only credit risk.
Risk premium is practically assumed to be none or constant.

We suppose that CDS spreads measure the sovereign credit risk of the concernedcountry’s debt.

Time series of SovCDS spread distributions

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Number of observations

Problems:

 Heavy-tailed distributions

Source: Markit Time-varying number of observations

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Method of distribution dependent index construction*
1 Apply the Box-Cox transformation (Box and Cox 1964) to the spreads
qi ,λ (n) = h( pi (n)) = λ−1 ( pi (n) λ − 1) λ ≠ 0

λ =0= log pi (n)2n = 1,..., T : timei = 1,..., k (n) : number of observations

For each λ, fit the following trend model to the mean time series yλ (n) of qi ,λ (n)∇ l tλ = vλ (n),vλ (n) ~ N (0,τλ2 )yλ (n) = tλ (n) + wλ (n), wλ (n) ~ N (0, σ λ (n) k (n))
2∇tλ (n) = tλ (n) − tλ (n − 1)σ λ (n) 2 is estimated by a time-varying variance model (Kitagawa 1987).

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Estimate parameters by applying state space modeling (Kitagawa 2010)
xλ ( n) = F xλ ( n − 1) + G vλ (n)yλ ( n) = H xλ ( n) + wλ ( n)4Determine an optimal λ by minimizing AIC 'λ : modified AICλ (Akaike 1973) to theoriginal spreads (Kitagawa 2010)
TAICλ ' = AICλ − 2∑ logn =15dhdz z = zλ ( n )dh: Jacobiandzzλ (n) = h −1 ( yλ (n))

An index is defined by the inverse Box-Cox transformation of the optimal trend.
* Improved version of Tanokura et al. 2012

5Countries of five regions

SovCDS spread distributions

MADE

AP

EELA

Source: Markit

Sovereign risk index and spread distributions

Asia Pacific (AP)Index & spread
distributions

Developed Europe(DE) Index & spread
distributions6

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Five regional sovereign risk indices

RISK

Source: Markit

Fit a multivariate AutoRegressive model andcalculate power contributions(PC)M

xn = ∑ Am xn − m + vnm =1

E (vn) = O, E (vn vn T ) = W ,E (vn vm T ) = O (n ≠ m),
E (vn xm T ) = O (n > m)

8xn : 5-dim stationary time series

Am : AR coefficient matrix
vn : 5-dim white noise

W : Variance covariance matrix

PC measures the influence between variable fluctuations of the noise at a frequency.
(Akaike 1968, Tanokura and Kitagawa 2004)
Power spectrum (PS) of A:
decomposes the fluctuation by frequency

PC of A:decomposes PS of A into components of variable combinations

9Power contributions (%)

Asia Pacific (AP) Dev. Europe (DE)

Emerg. Europe (EE) Mid. East/Africa (MA) Latin America (LA)self-contribution

self-contribution
self-contribution

self-contribution

self-contribution

Post-Lehman: 9/15/08 -11/16/09

T IME

Post-Greece: 11/17/09 -3/8/12

Current: 3/12/12 -3/29/13

Contribution score (CS)10...is defined as the quantity (% of the total) between two variables based on thesum of the equally allocated the PC value to variables concerned(at the dominant frequency domain of the power spectrum each region).

CS from Developed Europe can be regarded as the influence of the European
Worldwide spillover effects are almost found.
debt crisis.
CSs from Developed Europe for the current period become higher!

What happened inside the country in Dev. EuropeInflation (CPI)

Sovereign Risk (CDS)

Germany
IPI+CDS
CDS
Italy
CPI+CDS
CDS

Spain

Cyprus

Source: Markit,CEIC

Bipolarization of influence

Economy (IPI)

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Influence of sovereign risks between countries
Greece (GR)Cyprus (CY)

Post-Lehman: 9/15/08 -11/16/09

Italy (IT)Spain (SP)12

Germany (GE)IT+SP+GE

T IME

Post-Greece: 11/17/09 -3/8/12

Current: 3/12/12 -3/29/13

ALL-CY of Greece and prominence of Cyprus
Departure

CY+IT+SP+GE

CY+ITReferences
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