Recursive valuation of Basket Default Swaps

Iscoe, Ian; Kreinin, Alex

doi:10.21314/jcf.2006.153

Cited by 8 publications

(7 citation statements)

References 7 publications

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“…i is defined in the same form as a similar probability used to value BDS in [6] and [9] with T = 0. Therefore, we can use the method for BDS to compute the key probability Π (k) i with modified default probabilities.…”

Section: Pricing Equationsmentioning

confidence: 99%

“…Available methods for BDS include the convolution technique by Laurent and Gregory [10] and the recursive method based on the order statistics of individual default times by Iscoe and Kreinin [6]. Here we review the recursive method in [6] and use it in our numerical examples.…”

Section: Terminal Default Probabilitiesmentioning

confidence: 99%

“…For the mth-to-default BDS, Iscoe and Kreinin [6] derive the recursive relation between the mth-to-default and the (m − 1)st-to-default contracts:…”

Section: Terminal Default Probabilitiesmentioning

confidence: 99%

See 2 more Smart Citations

Fast Valuation of Forward-Starting Basket Default Swaps

Jackson

Kreinin²,

Zhang

2010

Int. J. Theor. Appl. Finan.

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A basket default swap (BDS) is a credit derivative with contingent payments that are triggered by a combination of default events of the reference entities. A forwardstarting basket default swap (FBDS) is a BDS starting at a specified future time.Existing analytic or semi-analytic methods for pricing FBDS are time consuming due to the large number of possible default combinations before the BDS starts. This paper develops a fast approximation method for FBDS based on the conditional independence framework. The method converts the pricing of a FBDS to an equivalent BDS pricing problem and combines Monte Carlo simulation with an analytic approach to achieve an effective method. This hybrid method is a novel technique which can be viewed either as a means to accelerate the convergence of Monte Carlo simulation or as a way to estimate parameters in an analytic method that are difficult to compute directly. Numerical results demonstrate the accuracy and efficiency of the proposed hybrid method.

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Section: Pricing Equationsmentioning

confidence: 99%

Section: Terminal Default Probabilitiesmentioning

confidence: 99%

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Fast Valuation of Forward-Starting Basket Default Swaps

Jackson

Kreinin²,

Zhang

2010

Int. J. Theor. Appl. Finan.

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“…The model was extended in Avellaneda and Zhu (2001). The literature on credit barrier models also includes working papers by Hyer et al (1999), Gordy and Heitfield (2001), Douady and Jeanblanc (2002) and Iscoe and Kreinin (2002).…”

Section: Introductionmentioning

confidence: 99%

Implied migration rates from credit barrier models

Albanese

Chen

2006

Journal of Banking & Finance

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“…Most authors have investigated numerical methods for finding the boundary. Details can be found in [6][7][8]15]. It is shown in [1] that for sufficiently smooth boundaries the density u(x, t) and the boundary b(t) are a solution of the following free boundary problem:…”

mentioning

confidence: 99%

Killed Brownian motion with a prescribed lifetime distribution and models of default

Ettinger¹,

Evans²,

Hening³

2014

Ann. Appl. Probab.

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The inverse first passage time problem asks whether, for a Brownian motion B and a nonnegative random variable ζ, there exists a time-varying barrier b such that P{Bs > b(s), 0 ≤ s ≤ t} = P{ζ > t}. We study a "smoothed" version of this problem and ask whether therewhere λ is a killing rate parameter, and ψ : R → [0, 1] is a nonincreasing function. We prove that if ψ is suitably smooth, the function t → P{ζ > t} is twice continuously differentiable, and the condition 0 < − d log P{ζ>t} dt < λ holds for the hazard rate of ζ, then there exists a unique continuously differentiable function b solving the smoothed problem. We show how this result leads to flexible models of default for which it is possible to compute expected values of contingent claims.

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Recursive valuation of Basket Default Swaps

Cited by 8 publications

References 7 publications

Fast Valuation of Forward-Starting Basket Default Swaps

Fast Valuation of Forward-Starting Basket Default Swaps

Implied migration rates from credit barrier models

Killed Brownian motion with a prescribed lifetime distribution and models of default

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