On the Pricing of Defaultable Bonds Using the Framework of Barrier Options

Ishizaka, Motokazu; Takaoka, Koichiro

doi:10.1007/s10690-005-6008-y

Cited by 6 publications

(5 citation statements)

References 10 publications

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“…Apuntamos también que este artículo se limita estrictamente al modelo de BC y, por lo tanto, no se discuten las generalizaciones posteriores como las de Longstaff & Schartz (1995) y Cathcart & El-Jahel (1998, que extendieron el modelo de BC considerando la tasa de interés como una variable estocástica, los de Fujita T. & Ishizaka M. (2002) e Ishizaka & Takaoka (2003) con la amortización de una deuda más realista, diferentes modelos de riesgo de crédito de Brigo & Tarenghi (2004), Brigo & Moroni (2006) y Nardon (2005), modelo del comercio con activos con riesgo de Holger Kraft & Mogens Steffensen, (2007), entre otros.…”

Section: Presentación De Resultados Principalesunclassified

Problema de calibración de mercado y estructura implícita del modelo de bonos de Black-Cox

Sukhomlin¹,

Jiménez

2016

RMCE

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El principal resultado de este artículo consiste en la resolución del problema inverso del modelo de Black-Cox (1976), usando el método propuesto por Sukhomlin (2007). Se parte del enfoque retrógrado (backward) para obtener una expresión exacta de la volatilidad implícita en función de parámetros cuantificables con datos de mercado y de variables conocidas. Se descubre la existencia de dos valores de la volatilidad para un activo subyacente en el modelo referido, lo que indica que las asunciones tradicionales no lo definen de manera unívoca. Se encuentra la causa de que el modelo de Black-Cox contenga dos valores de la volatilidad. Además, se lleva a cabo una simulación, a fin de verificar, numéricamente, que la expresión obtenida para la volatilidad es la inversión de la fórmula que representa la probabilidad de que la firma no alcance un nivel de insolvencia antes del tiempo de madurez de la deuda. Finalmente, se resuelve el problema de calibración de mercado desde el punto de vista directo (forward), encontrándose una expresión que resulta de mayor utilidad para los agentes de mercado.

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Section: Presentación De Resultados Principalesunclassified

Problema de calibración de mercado y estructura implícita del modelo de bonos de Black-Cox

Sukhomlin¹,

Jiménez

2016

RMCE

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“…However, with the strong influence of probabilistic methods in solving such PDEs, it is reasonable to consider parallel solution methods. One such approach is seen in the classical one factor models presented in Ishizaka and Takaoka (2003). By appealing to barrier option theory, the authors in Ishizaka and Takaoka (2003) utilize the measure Q with the Radon-Nikodym density process defined by the firm value A…”

Section: Bond Pricing In Stochastic Recovery Modelsmentioning

confidence: 99%

“…Computation of the PIT could involve the joint distribution of A T with quantities such as the running maximum, minimum, and average of A over the interval [t, T], among other quantities, depending on the new default set D. For example, one could consider the default time corresponding to the cumulative Parisian option, as detailed in Ishizaka and Takaoka (2003) and references within.…”

Section: Further Extensionsmentioning

confidence: 99%

A General Framework for Incorporating Stochastic Recovery in Structural Models of Credit Risk

Cohen

Costanzino²

2017

Risks

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Abstract:In this work, we introduce a general framework for incorporating stochastic recovery into structural models. The framework extends the approach to recovery modeling developed in Costanzino (2015, 2017) and provides for a systematic way to include different recovery processes into a structural credit model. The key observation is a connection between the partial information gap between firm manager and the market that is captured via a distortion of the probability of default. This last feature is computed by what is essentially a Girsanov transformation and reflects untangling of the recovery process from the default probability. Our framework can be thought of as an extension of Ishizaka and Takaoka (2003) and, in the same spirit of their work, we provide several examples of the framework including bounded recovery and a jump-to-zero model. One of the nice features of our framework is that, given prices from any one-factor structural model, we provide a systematic way to compute corresponding prices with stochastic recovery. The framework also provides a way to analyze correlation between Probability of Default (PD) and Loss Given Default (LGD), and term structure of recovery rates.

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“…Although default risks, credit risks, or counterparty risks for the pricing and hedging of derivatives, company securities, or underlying assets have all been discussed in the financial literature, few works have examined the default risk embodied in option contracts. In looking at financial research, these issues can be classified as defaultable bond problems (e.g., Merton, ; Moraux, ; Uhrig‐Homburg, ; Ishizaka & Takaoka, ), vulnerable option problems (e.g., Johnson & Stulz, ; Klein, ), bankruptcy and debt problems (see Acharya & Carpenter, ; Anderson & Sundaresan, ; Broadie, Chernov, & Sundaresan, ; François & Morellec, ; Leland, ; Leland & Toft, ; Mella‐Barral, ; Mella‐Barral & Perraudin, ), and counterparty risk problems (see Chang & Hung, ; Hull & White, ; Hung & Liu, ; Klein, , etc.). The above literature has not discussed the case of allowing option sellers to freely walk away from their obligations.…”

Section: Introductionmentioning

confidence: 99%

Valuing Seller‐Defaultable Options

Chen

Hwang

et al. 2012

Journal of Futures Markets

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This study analyzes seller-defaultable options that allow option writers to have a free-will right to default, along with some prespecified default mechanisms. We analytically and numerically examine the pricing, hedging, defaulting, and profitability of the seller-defaultable options, considering three possible scenarios for seller default. Analyzing the essential implications of seller-defaultable options, we show that the option price is positively correlated with the default fine, underlying asset price, and volatility. The seller-defaultable option's Greeks appear more complicated than those of the plain vanilla options. The likelihood of sellers The authors would like to thank anonymous referees and the editor for their helpful comments. The authors alone remain responsible for any errors in connection with this work.

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On the Pricing of Defaultable Bonds Using the Framework of Barrier Options

Cited by 6 publications

References 10 publications

Problema de calibración de mercado y estructura implícita del modelo de bonos de Black-Cox

Problema de calibración de mercado y estructura implícita del modelo de bonos de Black-Cox

A General Framework for Incorporating Stochastic Recovery in Structural Models of Credit Risk

Valuing Seller‐Defaultable Options

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