An empirical analysis of alternative recovery risk models and implied recovery rates

Zhang, Frank Xiaoling

doi:10.1007/s11147-009-9046-1

Cited by 3 publications

(5 citation statements)

References 34 publications

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“…Remark 2 (a) Advantage of (5) is consistent with extant empirical evidences (see e.g., Jarrow [15]; Altman et al [16]; Bakshi et al [17]; Zhang [18], for reviews). Moreover, the recovery rate is negatively related to the default rate, that is,…”

Section: Assumptionssupporting

confidence: 80%

“…Moreover, b 2 ( t ) is a time‐varying deterministic function, W λ ( t ) is another Q ‐standard Brownian motion, and it is dependent on W r ( t ) with a correlation coefficient ρ ( t ), that is, C o v (d W r ( t ),d W λ ( t )) = ρ ( t )d t ,| ρ ( t )| < 1.(4) If the default occurs at time t < T , then the bondholder receives a fraction R ( λ ( t )) of the default‐free zero‐coupon bond paying 1 at time T , where R ( λ ( t )) denotes the recovery rate and is stochastic. Following the Bakshi–Madan–Zhang recovery model, we assume that R ( λ ( t )) has the following form:

R (λ (t)) = R_{0} + R_{1} {normale}^{- \frac{λ (t)}{2 a_{2}}},

where R 0 and R 1 are nonnegative constants, and 0≤ R 0 + R 1 ≤1.Applying Ito's lemma to R ( λ ( t )), we have

normald R (λ (t)) = - \frac{R_{1}}{2 a_{2}} {normale}^{- \frac{λ (t)}{2 a_{2}}} ({}, ([], a_{2} (b_{2} (t) - λ (t)) - \frac{σ_{2}^{2}}{4 a_{2}}) normald t + σ_{2} normald W_{λ} (t)) .

Remark (a) Advantage of is consistent with extant empirical evidences (see e.g., Jarrow ; Altman et al ; Bakshi et al ; Zhang , for reviews). Moreover, the recovery rate is negatively related to the default rate, that is,

\frac{normald R (λ (t))}{normald λ (t)} = - \frac{R_{1}}{2 a_{2}} {normale}^{- \frac{λ (t)}{2 a_{2}}} < 0

.…”

Section: Mathematical Model For Pricing Defaultable Bondsmentioning

confidence: 99%

“…Following the works of Altman et al [16], Bakshi et al [17] and Zhang [18] propose a recovery rate model which can capture the negative correlation with the default rate. This recovery rate model is defined as…”

Section: Introductionmentioning

confidence: 99%

“…Following the works of Altman et al , Bakshi et al and Zhang propose a recovery rate model which can capture the negative correlation with the default rate. This recovery rate model is defined as

w (t) = w_{0} + w_{1} e^{- [Λ_{0} + Λ_{1} r (t)]},

where w 0 and w 1 are nonnegative constants, and 0≤ w 0 + w 1 ≤1.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A reduced‐form model for pricing defaultable bonds and credit default swaps with stochastic recovery

Pan

2016

Appl Stoch Models Bus & Ind

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This paper presents a reduced-form model for pricing defaultable bonds and credit default swaps (CDSs) with stochastic recovery, where the recovery risk is coupled with the default intensity, while the default intensity is described by a stochastic differential equation. Closed-form pricing formulae for defaultable bonds and CDSs are obtained by applying variable change techniques and partial differential equation approaches. The closed-form pricing formulae can provide valuable assistance in analyzing certain complications associated with portfolio management and hedging analysis. Finally, numerical experiments are provided to illustrate how the recovery parameters and intensity parameters affect the credit spread of a defaultable bond and the swap premium of a CDS. Appl. Stochastic Models Bus. Ind. 2016, 32 725-739 H t = 1 ⩽t is the point processes generated by only default time . Moreover, Q is a risk-neutral probability measure. For more details, we refer to Elliott et al. [23] and the reference therein. Under this probability space, our model assumptions are as follows: 726 Appl. Stochastic Models Bus. Ind. 2016, 32 725-739 J. PAN AND Q. XIAO e − (t) 2a 2 < 0. (b) If we let R 1 = 0 in Equation (5), then this stochastic recovery model degenerates into a constant recovery model, which exists in most studies.

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Section: Assumptionssupporting

confidence: 80%

R (λ (t)) = R_{0} + R_{1} {normale}^{- \frac{λ (t)}{2 a_{2}}},

where R 0 and R 1 are nonnegative constants, and 0≤ R 0 + R 1 ≤1.Applying Ito's lemma to R ( λ ( t )), we have

normald R (λ (t)) = - \frac{R_{1}}{2 a_{2}} {normale}^{- \frac{λ (t)}{2 a_{2}}} ({}, ([], a_{2} (b_{2} (t) - λ (t)) - \frac{σ_{2}^{2}}{4 a_{2}}) normald t + σ_{2} normald W_{λ} (t)) .

\frac{normald R (λ (t))}{normald λ (t)} = - \frac{R_{1}}{2 a_{2}} {normale}^{- \frac{λ (t)}{2 a_{2}}} < 0

.…”

Section: Mathematical Model For Pricing Defaultable Bondsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

w (t) = w_{0} + w_{1} e^{- [Λ_{0} + Λ_{1} r (t)]},

where w 0 and w 1 are nonnegative constants, and 0≤ w 0 + w 1 ≤1.…”

Section: Introductionmentioning

confidence: 99%

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A reduced‐form model for pricing defaultable bonds and credit default swaps with stochastic recovery

Pan

2016

Appl Stoch Models Bus & Ind

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“…The assumption of a constant recovery rate is inadequate for pricing senior tranches, as it can imply the tranches are free from default risk. Zhang (2010) specifies the recovery rate to depend on the intensity function…”

Section: Recovery Ratesmentioning

confidence: 99%

Counterparty Risk: A Review

Turnbull

2014

Annu. Rev. Financ. Econ.

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This review provides formal definitions of the terms credit value adjustment (CVA) and debt value adjustment (DVA). Estimating these quantities requires modeling the probabilities of default and the loss given default, recognizing the dependence structure among all these inputs. In practice, marginal distributions are used and a copula function assumed. Although it has long been known that different copula functions can produce very different price estimates, keeping marginal distributions constant, there is little empirical evidence about the appropriate form of function to use for modeling default dependence. This review discusses the use of collateral for risk mitigation and its effects on CVA. Regulators have argued that standardized contracts should be cleared through central counterparties (CCPs). However, there are arguments against CCPs.

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Does modeling framework matter? A comparative study of structural and reduced-form models

Gündüz

Uhrig‐Homburg

2013

Rev Deriv Res

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This study provides a rigorous empirical comparison of structural and reduced-form credit risk frameworks. As major difference we focus on the discriminative modeling of default time. In contrast to previous literature, we calibrate both approaches to bond and equity prices. By using same input data, applying comparable estimation techniques, and assessing the out-of-sample prediction quality on same time series of CDS prices we are able to judge whether empirically the model structure itself makes an important difference. Interestingly, the models' prediction power is quite close on average. Still, the reduced-form approach outperforms the structural for investment-grade names and longer maturities. JEL Classification: G13Keywords: Credit risk, structural models, reduced-form models, default intensity, stationary leverage, credit default swaps. Non-technical SummaryIn the financial industry, applying the Black/Scholes option pricing framework for pricing purposes has been widely accepted as the benchmark model for equity and FX derivatives.However, no single agreed pricing model has emerged that could serve as a benchmark for instruments that are exposed to credit risk. The literature differentiates between structural models that are based on modeling of the evolution of the balance sheet of the issuer, and reduced-form models that specify credit risk exogenously by a default intensity process.Until now, there has been no common agreement in academia and in the financial industry on which model framework better captures credit risk. In previous studies, even when testing the same model, the use of different datasets has contributed to quite different results. This study overcomes this issue by applying the same dataset to structural and reduced-form approaches. Leverage has been used as a key credit risk factor that could be explanatory in both frameworks. By using the same input data, applying comparable estimation techniques and assessing the out-of-sample prediction quality on the same time series of CDS prices, we are able to judge whether empirically the model structure itself makes an important difference. The models' predictive power is quite close on average, indicating that for pricing purposes the modeling type does not matter compared to the input data used. Still, the reduced-form approach outperforms the structural approach for investment-grade names and longer maturities. In contrast, the structural approach performs better for shorter maturities and sub-investment grade names. The study concludes that both frameworks provide CDS price prediction results equally well if a basis of comparison can be provided. These results have implications on choosing appropriate risk measurement techniques in financial markets.

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An empirical analysis of alternative recovery risk models and implied recovery rates

Abstract: Recovery, Default risk, Defaultable bonds, Corporate bond pricing, Recovery payout as a fraction of face, Recovery as a fraction of pre-default debt values, Recovery as a fraction of the present value of face, Implied recovery, G0, G10, G11, G12, G13, C5,

Cited by 3 publications

References 34 publications

A reduced‐form model for pricing defaultable bonds and credit default swaps with stochastic recovery

A reduced‐form model for pricing defaultable bonds and credit default swaps with stochastic recovery

Counterparty Risk: A Review

Does modeling framework matter? A comparative study of structural and reduced-form models

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