A jump to default extended CEV model: an application of Bessel processes

Carr, Peter; Linetsky, Vadim

doi:10.1007/s00780-006-0012-6

Cited by 207 publications

(267 citation statements)

References 40 publications

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“…The next proposition offers the closed-form solutions for the hedge ratios of the pricing solutions proposed by Carr and Linetsky (2006), which represent a novel contribution to the credit and equity derivatives literature. 8…”

Section: Hedge Ratiosmentioning

confidence: 99%

“…11 The proxy of the exact American option price (4th column) is computed through the Crank-Nicolson finite-difference scheme with 15, 000 time intervals and 10, 000 space steps. The optimal stopping approach of Nunes (2009) is implemented with conditional minimization through the Matlab "fmincon" algorithm, and using a four and five degree polynomial specification 10 The use of the Nunes (2009) valuation methodology will also allow us to compare the SHP results to be obtained under the JDCEV model proposed in Carr and Linetsky (2006).…”

Section: Cev Modelmentioning

confidence: 99%

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Pricing and static hedging of American-style options under the jump to default extended CEV model

Ruas

Dias

Nunes

2013

Journal of Banking & Finance

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Section: Hedge Ratiosmentioning

confidence: 99%

Section: Cev Modelmentioning

confidence: 99%

Pricing and static hedging of American-style options under the jump to default extended CEV model

Ruas

Dias

Nunes

2013

Journal of Banking & Finance

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“…Our equity-based model contributes also to credit risk management by being conducive to closed forms for the objective default probability 14 , V P (S, T, 0), 14 For example, the New Basel Capital Accord allows the use of model-based objective probabilities of default to determine the appropriate level of reserves to support credit risky activities.…”

Section: Propositionmentioning

confidence: 99%

Assessing Credit with Equity: A CEV Model with Jump to Default

2005

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Unlike in structural and reduced-form models, we use equity as a liquid and observable primitive to analytically value corporate bonds and credit default swaps. Restrictive assumptions on the firm's capital structure are avoided. Default is parsimoniously represented by equity value hitting the zero barrier. Default can be either predictable, according to a CEV process that yields a positive probability of diffusive default and enables the leverage effect, or unpredictable, according to a Poisson-process jump that implies non-zero credit spreads for short maturities. Easy cross-asset hedging is enabled. By means of a carefully specified pricing kernel, we also enable analytical credit-risk management under possibly systematic jump-to-default risk.JEL-Classification: G12, G33.

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“…Hull and White (1989), Stein and Stein (1991), Heston (1993) introduced analytical models with stochastic volatility. Carr and Linetsky (2006), Aboulaich et al (2013) investigated the stochastic volatility model with jumps. The CEV model is a generalization of dynamic volatility models.…”

Section: Introductionmentioning

confidence: 99%

Spectral study of options based on CEV model with multidimensional volatility

Burtnyak

Malytska

2018

Investment Management and Financial Innovations

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This article studies the derivatives pricing using a method of spectral analysis, a theory of singular and regular perturbations. Using a risk-neutral assessment, the authors obtain the Cauchy problem, which allows to calculate the approximate price of derivative assets and their volatility based on the diffusion equation with fast and slow variables of nonlocal volatility, and they obtain a model with multidimensional stochastic volatility. Applying a spectral theory of self-adjoint operators in Hilbert space and a theory of singular and regular perturbations, an analytic formula for approximate asset prices is established, which is described by the CEV model with stochastic volatility dependent on l-fast variables and r-slowly variables, l ≥ 1, r ≥ 1, l ∈ N, r ∈ N and a local variable. Applying the Sturm-Liouville theory, Fredholm’s alternatives, as well as the analysis of singular and regular perturbations at different time scales, the authors obtained explicit formulas for derivatives price approximations. To obtain explicit formulae, it is necessary to solve 2l Poisson equations.

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A jump to default extended CEV model: an application of Bessel processes

Abstract: Default, Credit spread, Corporate bonds, Equity derivatives, Credit derivatives, Implied volatility skew, CEV model, Bessel processes, 60J35, 60J60, 60J65, 60G70, G12, G13,

Cited by 207 publications

References 40 publications

Pricing and static hedging of American-style options under the jump to default extended CEV model

Pricing and static hedging of American-style options under the jump to default extended CEV model

Assessing Credit with Equity: A CEV Model with Jump to Default

Spectral study of options based on CEV model with multidimensional volatility

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