An extension of CreditGrades model approach with Lévy processes

Ozeki, Takaaki; Umezawa, Yuji; Yamazaki, Akira; Yoshikawa, Daisuke

doi:10.1080/14697681003777089

Cited by 5 publications

(2 citation statements)

References 26 publications

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“…See Finger et al (2002), and Stamicar and Finger (2005) for details of the CreditGrades model, and also Sepp (2006), and Ozeki et al (2010) for extensions with stochastic volatility and jumps.…”

Section: Setupmentioning

confidence: 99%

A note on the Black–Scholes implied volatility with default risk

Ohsaki¹,

Ozeki

Umezawa

et al. 2010

Wilmott Journal

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This paper focuses on a theoretical aspect of relations between the Black-Scholes implied volatility and the default probability in a general framework that the stock price is fixed at zero after default occurs. It is shown that the default probability of the company under a riskneutral measure significantly links to the implied volatility skew atWe consider European call and put options with default risk. Let C(K, T) and P(K, T) denote call and put prices with strike K and maturity T at time t = 0 respectively. Then, the call and the put prices under the assumption (1) can be written aswhere E[ · ] is an expectation operator under Q. The following lemma shows that default and survival probabilities can be expressed as the first derivative of the put and the call with respect to strike K at K = 0.Lemma 1 The partial differentials ∂P(K, T)/∂K and ∂C(K, T)/∂K exist for all K ≥ 0. Moreover, the risk-neutral default and survival probabilities of a reference company are given byand Q(τ > T) = −e rT ∂C(K, T) ∂Krespectively for any T > 0.

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Section: Setupmentioning

confidence: 99%

A note on the Black–Scholes implied volatility with default risk

Ohsaki¹,

Ozeki

Umezawa

et al. 2010

Wilmott Journal

Self Cite

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“…The Credit-Grades model introduced by Finger et al [20] and Stamicar and Finger [44] is one of the most preferred structural models for practitioners when jointly pricing credit default swaps and equity plain vanilla options, and there are several extensions of the CreditGrades model; e.g., see Sepp [43] and Ozeki et al [37]. Section 5 will show an application of our static hedging scheme to an extended CreditGrades model to replicate defaultable bonds.…”

Section: Introductionmentioning

confidence: 99%

Static Hedging of Defaultable Contingent Claims: A Simple Hedging Scheme Across Equity and Credit Markets

Ohsaki¹,

Yamazaki

2011

Int. J. Theor. Appl. Finan.

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This paper proposes a simple scheme for static hedging of defaultable contingent claims. It generalizes the techniques developed by Carr and Chou (1997), , and Takahashi and Yamazaki (2009a) to credit-equity models. Our scheme provides a hedging strategy across credit and equity markets, where suitable defaultable contingent claims are accurately replicated by a feasible number of plain vanilla equity options. Another point is that shorter maturity options are available to hedge longer maturity defaultable contingent claims. Through numerical examples, it is shown that the scheme is applicable to both structural and intensity-based models.

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Credit-Equity Modeling Under a Latent Lévy Firm Process

Kijima

Siu

2014

Int. J. Theor. Appl. Finan.

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Recent empirical studies have demonstrated the informative nature of the equity returns in explaining the variation of the underlying firm's credit default swap (CDS) spreads. Motivated by these findings, we propose a unified credit-equity model by extending the latent structural model in Kijima et al. (2009). As in the original latent model, we treat the actual status of the firm to be unobservable and one can extract information from the marker process that is observable to the investors. Default occurs when the actual firm value drops below a default threshold for the first time. Different from the model in Kijima et al. (2009), however, we define the marker process to be the firm's equity process. Choosing firm's equity process to be a marker process subsequently relaxes the restrictions imposed in Kijima et al. (2009), enabling us to price firm-related securities. Additionally, we enrich the original latent structural model with jump and regime-switching dynamics. The purpose of the extensions is to capture more realistic credit spreads and implied volatility skews under different economic environments. The proposed model maintains analytical tractability even under such complex dynamics, for the prices of CDSs and equity options admit semi-closed-form solutions. In sum, our model can evaluate corporate securities and their derivatives in a unified framework.

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An extension of CreditGrades model approach with Lévy processes

Cited by 5 publications

References 26 publications

A note on the Black–Scholes implied volatility with default risk

A note on the Black–Scholes implied volatility with default risk

Static Hedging of Defaultable Contingent Claims: A Simple Hedging Scheme Across Equity and Credit Markets

Credit-Equity Modeling Under a Latent Lévy Firm Process

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