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

Content Provider	Springer Nature Link
Author	Linetsky, Vadim Carr, Peter
Copyright Year	2006
Abstract	We develop a flexible and analytically tractable framework which unifies the valuation of corporate liabilities, credit derivatives, and equity derivatives. We assume that the stock price follows a diffusion, punctuated by a possible jump to zero (default). To capture the positive link between default and equity volatility, we assume that the hazard rate of default is an increasing affine function of the instantaneous variance of returns on the underlying stock. To capture the negative link between volatility and stock price, we assume a constant elasticity of variance (CEV) specification for the instantaneous stock volatility prior to default. We show that deterministic changes of time and scale reduce our stock price process to a standard Bessel process with killing. This reduction permits the development of completely explicit closed form solutions for risk-neutral survival probabilities, CDS spreads, corporate bond values, and European-style equity options. Furthermore, our valuation model is sufficiently flexible so that it can be calibrated to exactly match arbitrarily given term structures of CDS spreads, interest rates, dividend yields, and at-the-money implied volatilities.
Ending Page	330
Page Count	28
Starting Page	303
File Format	PDF
ISSN	09492984
e-ISSN	14321122
Journal	Finance and Stochastics
Issue Number	3
Volume Number	10
Language	English
Publisher	Springer-Verlag
Publisher Date	2006-08-15
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Equity derivatives Finance /Banking Diffusion processes Probability Theory and Stochastic Processes Transition functions, generators and resolvents Default Quantitative Finance Bessel processes Brownian motion Corporate bonds Credit spread Extreme value theory; extremal processes Statistics for Business/Economics/Mathematical Finance/Insurance Economic Theory Credit derivatives CEV model Implied volatility skew
Content Type	Text
Resource Type	Article
Subject	Finance Statistics and Probability Statistics, Probability and Uncertainty

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Pricing equity default swaps under the jump-to-default extended CEV model

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