Basel requirements of downturn loss given default: modeling and estimating probability of default and loss given default correlations

Miu, Peter; Ozdemir, Bogie

doi:10.21314/jcr.2006.037

Cited by 54 publications

(41 citation statements)

References 5 publications

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“…), one simply needs a model for default τ and need not concern themselves with modeling recovery in the event of default. In this paper, we explicitly model recovery and remove the constant recovery assumption in CDS pricing thereby valuing the protection leg of the CDS using (5) directly rather than (6).…”

Section: B Tt = Nd(t T) P T [τ > T] + F E T [D(t τ)A τ 1 {τ≤T} ]mentioning

confidence: 99%

“…For instance, Giese [3] incorporates PG-LGD correlations into a single-factor Vasicek framework and finds that capital increases by up to 35% at the 99.9% confidence interval for high-yield credit portfolios. While investigating stressed LGDs, Miu and Ozdemir [6] find that in order to compensate for neglecting the PD-LGD correlation in credit capital modeling, the mean LGD must be increased by about 37% from its unbiased estimate in order to compensate for the lack of correlations.…”

Section: Modeling Recovery Risk Within a Structural Frameworkmentioning

confidence: 99%

“…However, there is a large body of empirical evidence showing that recovery rates are inversely correlated with probabilities of default [1,14,27,[29][30][31][32][33][34] and so recovery risk is a real financial phenomena that should be modeled. Second, this correlation can have a very large effect on credit capital [5,6]. Ignoring this effect in a pricing model could potentially lead to large mispricings or significant misestimation of risk.…”

Section: Modeling Recovery Risk Within a Structural Frameworkmentioning

confidence: 99%

“…The spread-ratio (98) is the Stochastic Recovery Black-Cox model implementation of Equation (6) in [14] used to extract recovery risk premiums from empirical data.…”

Section: Remarkmentioning

confidence: 99%

“…This phenomena has been successfully incorporated into recent economic capital models (c.f. [2][3][4][5][6][7]) but still hasn't enjoyed mainstream adoption in pricing models. One notable exception has been in CDO pricing, where stochastic recovery has been added to many legacy models.…”

mentioning

confidence: 99%

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Bond and CDS Pricing via the Stochastic Recovery Black-Cox Model

Cohen

Costanzino²

2017

Risks

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Building on recent work incorporating recovery risk into structural models by Cohen & Costanzino (2015), we consider the Black-Cox model with an added recovery risk driver. The recovery risk driver arises naturally in the context of imperfect information implicit in the structural framework. This leads to a two-factor structural model we call the Stochastic Recovery Black-Cox model, whereby the asset risk driver A t defines the default trigger and the recovery risk driver R t defines the amount recovered in the event of default. We then price zero-coupon bonds and credit default swaps under the Stochastic Recovery Black-Cox model. Finally, we compare our results with the classic Black-Cox model, give explicit expressions for the recovery risk premium in the Stochastic Recovery Black-Cox model, and detail how the introduction of separate but correlated risk drivers leads to a decoupling of the default and recovery risk premiums in the credit spread. We conclude this work by computing the effect of adding coupons that are paid continuously until default, and price perpetual (consol bonds) in our two-factor firm value model, extending calculations in the seminal paper by Leland (1994). Background and MotivationMost legacy credit models assume that recovery is a constant. It is well known, however, that recovery rates are not constant and indeed are correlated to a variety of risk drivers, including default and interest rates. For example, in their study on real-world recovery rates, Altman et al. [1] show that realized recovery rates are inversely proportional to realized default rates. This phenomena has been successfully incorporated into recent economic capital models (c.f. [2][3][4][5][6][7]) but still hasn't enjoyed mainstream adoption in pricing models. One notable exception has been in CDO pricing, where stochastic recovery has been added to many legacy models. This was necessary after the most recent credit-liquidity crisis, whereby for a period of time it was not possible to calibrate standard CDO models to the complete set of CDX.IG and ITRAXX.IG tranche quotes. The inability to calibrate the standard CDO models has been attributed to the assumption that recovery at default is deterministic, and does not depend on time or state variables. This has led to adding stochastic recovery to CDO models (c.f. [8][9][10][11][12][13]), which is now standard practice in industry.However, stochastic recovery has not yet received equally widespread interest and acceptance for other credit products such as defaultable bonds, credit default swaps and credit linked notes. In fact, there are a dearth of pricing formulas for credit products where recovery is modeled explicitly. This has become commonplace even though recovery is clearly a key component in the determination of credit spreads [14]. One recent approach to stochastic recovery modeling can be found in [15]. Take for example bond pricing, where the price of a zero-coupon defaultable bond is given by the risk-neutral expected present value of the payoff ...

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Section: B Tt = Nd(t T) P T [τ > T] + F E T [D(t τ)A τ 1 {τ≤T} ]mentioning

confidence: 99%

Section: Modeling Recovery Risk Within a Structural Frameworkmentioning

confidence: 99%

Section: Modeling Recovery Risk Within a Structural Frameworkmentioning

confidence: 99%

“…The spread-ratio (98) is the Stochastic Recovery Black-Cox model implementation of Equation (6) in [14] used to extract recovery risk premiums from empirical data.…”

Section: Remarkmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Bond and CDS Pricing via the Stochastic Recovery Black-Cox Model

Cohen

Costanzino²

2017

Risks

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Default Recovery Rates and LGD in Credit Risk Modeling and Practice

2008

Managing Credit Risk

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Evidence from many countries in recent years suggests that collateral values and recovery rates on corporate defaults can be volatile and, moreover, that they tend to go down just when the number of defaults goes up in economic downturns. This link between recovery rates and default rates has traditionally been neglected by credit risk models, as most of them focused on default risk and adopted static loss assumptions, treating the recovery rate either as a constant parameter or as a stochastic variable independent from the probability of default. This traditional focus on default analysis has been partly reversed by the recent significant increase in the number of studies dedicated to the subject of recovery rate estimation and the relationship between default and recovery rates. This paper presents a detailed review of the way credit risk models, developed during the last thirty years, treat the recovery rate and, more specifically, its relationship with the probability of default of an obligor. We also review the efforts by rating agencies to formally incorporate recovery ratings into their assessment of corporate loan and bond credit risk and the recent efforts by the Basel Committee on Banking Supervision to consider "downturn LGD" in their suggested requirements under Basel II. Recent empirical evidence concerning these issues and the latest data on high-yield bond and leverage loan defaults is also presented and discussed.

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Cyclicality in losses on bank loans

Keijsers

Diris

Kole

2018

J of Applied Econometrics

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Basel requirements of downturn loss given default: modeling and estimating probability of default and loss given default correlations

Cited by 54 publications

References 5 publications

Bond and CDS Pricing via the Stochastic Recovery Black-Cox Model

Bond and CDS Pricing via the Stochastic Recovery Black-Cox Model

Default Recovery Rates and LGD in Credit Risk Modeling and Practice

Cyclicality in losses on bank loans

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