Friday, October 5, 2012: 10:00 AM
Abstract. During the European nancial crisis strong correlations of certain sovereigns'
credit spreads were frequently observed even though in many cases the respective
economies are hardly connected in real economic terms. A possible explanation for
this phenomon might be that the increase of these spreads is not induced by an
increase in default probabilities themselves but by an increase of their implied vari-
ances. The latter could, for example, be caused by a market reassessment of the
information quality provided by sovereign institutions. To analyze this hypothetical
relation, we model the risk-neutral default probabilities implied in credit default
swap (CDS) spreads both under the risk-neutral and historical measure considering
a default as rst jump of a Poisson process and the intensities as possible mean
reverting di usion processes (see Pan and Singleton, 2008). By comparing di u-
sion parameter estimates obtained under both of these measures, we expect to see
whether an increase in sovereign credit spreads can be explained by an increase in
risk-premiums for the default intensity variance. We exploit that many di usions
belong to the class of ane processes for numerically extracting the implied intensi-
ties in a comfortable manner. We thereby apply the results of Due et al (2001) to
transform the Feynman-Kac di erential equations related to the expectation terms
that are part of the common CDS-pricing formula. We moreover suggest an iterative
procedure to solve numerically for the implied intensities based on the parameters
of the underlying di usions and to estimate the di usion parameters based on the
obtained default intensities in turn.
credit spreads were frequently observed even though in many cases the respective
economies are hardly connected in real economic terms. A possible explanation for
this phenomon might be that the increase of these spreads is not induced by an
increase in default probabilities themselves but by an increase of their implied vari-
ances. The latter could, for example, be caused by a market reassessment of the
information quality provided by sovereign institutions. To analyze this hypothetical
relation, we model the risk-neutral default probabilities implied in credit default
swap (CDS) spreads both under the risk-neutral and historical measure considering
a default as rst jump of a Poisson process and the intensities as possible mean
reverting di usion processes (see Pan and Singleton, 2008). By comparing di u-
sion parameter estimates obtained under both of these measures, we expect to see
whether an increase in sovereign credit spreads can be explained by an increase in
risk-premiums for the default intensity variance. We exploit that many di usions
belong to the class of ane processes for numerically extracting the implied intensi-
ties in a comfortable manner. We thereby apply the results of Due et al (2001) to
transform the Feynman-Kac di erential equations related to the expectation terms
that are part of the common CDS-pricing formula. We moreover suggest an iterative
procedure to solve numerically for the implied intensities based on the parameters
of the underlying di usions and to estimate the di usion parameters based on the
obtained default intensities in turn.
References
DUFFIE, D., PAN, J. und SINGLETON, K. (2000): Transform Analysis and Asset
Pricing for Ane Jump Di usions. Econometrica, 68, 1343-1376.
PAN, J. und SINGLETON, K. (2008): Default and Recovery Implicit in the Term
Structure of Sovereign CDS Spreads. Journal of Finance, LXIII, 2345-2384