A Remark on default risk models

Kusuoka, Shigeo

doi:10.1007/978-4-431-65895-5_5

Cited by 186 publications

(158 citation statements)

References 2 publications

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“…This is the case of the models of Kusuoka (1999), Jarrow & Yu (2001), Yu (2007), where the intensities are affine functions of the default indicators 4 .…”

Section: Intensity Specificationmentioning

confidence: 99%

Hedging default risks of CDOs in Markovian contagion models

Laurent

Cousin

Fermanian

2010

Quantitative Finance

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We describe a hedging strategy of CDO tranches based upon dynamic trading of the corresponding credit default swap index. We rely upon a homogeneous Markovian contagion framework, where only single defaults occur. In our framework, a CDO tranche can be perfectly replicated by dynamically trading the credit default swap index and a risk-free asset. Default intensities of the names only depend upon the number of defaults and are calibrated onto an input loss surface. Moreover, numerical implementation can be carried out fairly easily thanks to a recombining tree describing the dynamics of the aggregate loss. Both continuous time market and its discrete approximation are complete. The computed credit deltas can be seen as a credit default hedge and may also be used as a benchmark to be compared with the market credit deltas.

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“…This is the case of the models of Kusuoka (1999), Jarrow & Yu (2001), Yu (2007), where the intensities are affine functions of the default indicators 4 .…”

Section: Intensity Specificationmentioning

confidence: 99%

Hedging default risks of CDOs in Markovian contagion models

Laurent

Cousin

Fermanian

2010

Quantitative Finance

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“…Such setups arise, e.g., in the presence of counterparty risk (as in Kusuoka (1999) and Jarrow and Yu (2001)) or contagion (as in Collin-Dufresne, Goldstein, and Helwege (2003)). …”

Section: Default Risk Premiamentioning

confidence: 99%

“…20 Cases in which the doubly stochastic setting no longer holds are studied in Duffie, Schroder, and Skiadas (1996), Kusuoka (1999), Jarrow and Yu (2001), Collin-Dufresne, Goldstein, and Helwege (2003) and to the assumption inherent in the Cox process setup that the filtration generated by the default components is conditionally independent of the default event, there do not exist feedback effects from the default time into the default components to be considered in the valuation.…”

Section: Default Risk Premiamentioning

confidence: 99%

The Economic Role of Jumps and Recovery Rates in the Market for Corporate Default Risk

Schneider¹,

Sögner²,

Veža³

2010

J. Financ. Quant. Anal.

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A previous version of this paper was circulated as "Jumps and Recovery Rates Inferred from Corporate CDS Premia". We are thankful to FIRM@WU for access to their high-performance computing resources as well as friendly support, and to Dow Jones for providing us with complete ICB sector information. AbstractUsing an extensive cross-section of US corporate CDS this paper offers an economic understanding of implied loss given default (LGD) and jumps in default risk. We formulate and underpin empirical stylized facts about CDS spreads, which are then reproduced in our affine intensity-based jump-diffusion model. Implied LGD is well identified, with obligors possessing substantial tangible assets expected to recover more. Sudden increases in the default risk of investment-grade obligors are higher relative to speculative grade. The probability of structural migration to default is low for investment-grade and heavily regulated obligors because investors fear distress rather through rare but devastating events.

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“…As mentioned before the proposition, the fact that the default time depends on the value of the defaultable security forces us to construct τ, P, and S simultaneously. In order to do so, we rely on a change of measure argument similar to that of Kusuoka (1999). More precisely, we start from an exogenously specified probability measure under which the intensity of the default time is constant, then construct the value process S, and finally define P by a suitably chosen equivalent change of probability measure.…”

Section: Recursive Valuation Of Defaultable Securitiesmentioning

confidence: 99%

“…As a third example, we revisit the counterparty credit risk model that was first investigated by Jarrow and Yu (2001), henceforth (JY), and Kusuoka (1999).…”

Section: Counterparty Credit Riskmentioning

confidence: 99%

A General Formula for Valuing Defaultable Securities

2004

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Previous research has shown that under a suitable no-jump condition, the price of a defaultable security is equal to its risk-neutral expected discounted cash flows if a modified discount rate is introduced to account for the possibility of default. Below, we generalize this result by demonstrating that one can always value defaultable claims using expected risk-adjusted discounting provided that the expectation is taken under a slightly modified probability measure. This new probability measure puts zero probability on paths where default occurs prior to the maturity, and is thus only absolutely continuous with respect to the risk-neutral probability measure. After establishing the general result and discussing its relation with the existing literature, we investigate several examples for which the no-jump condition fails. Each example illustrates the power of our general formula by providing simple analytic solutions for the prices of defaultable securities.

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A Remark on default risk models

Cited by 186 publications

References 2 publications

Hedging default risks of CDOs in Markovian contagion models

Hedging default risks of CDOs in Markovian contagion models

The Economic Role of Jumps and Recovery Rates in the Market for Corporate Default Risk

A General Formula for Valuing Defaultable Securities

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