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Pricing the Zero-Coupon Bond and its Fair Premium Under a Structural Credit Risk Model with Jumps

Part of: Markov processes Integral transforms, operational calculus

Published online by Cambridge University Press:  14 July 2016

Yinghui Dong ,
Guojing Wang  and
Rong Wu
Yinghui Dong*
Affiliation:
Suzhou University and Suzhou University of Science and Technology
Guojing Wang*
Affiliation:
Suzhou University
Rong Wu*
Affiliation:
Nankai University
*
∗Postal address: Department of Mathematics and Center for Financial Engineering, Suzhou University, Suzhou 215006, P. R. China.
∗Postal address: Department of Mathematics and Center for Financial Engineering, Suzhou University, Suzhou 215006, P. R. China.
∗∗∗Postal address: Department of Mathematics and LPMC, Nankai University, Tianjin 300071, P. R. China.
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Abstract

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In this paper we consider a structural form credit risk model with jumps. We investigate the credit spread, the price, and the fair premium of the zero-coupon bond for the proposed model. The price and the fair premium of the bond are associated with the Laplace transform of default time and the firm's expected present market value at default. We give sufficient conditions under which the Laplace transform and the expected present market value of a firm at default are twice continuously differentiable. We derive closed-form expressions for them when the jumps have a hyperexponential distribution. Using the closed-form expressions, we obtain numerical solutions for the default probability, the credit spread, and the fair premium of the bond.

Keywords

Credit spreaddefault probabilityhyperexponential distributionfair premium ratestructural credit risk modelzero-coupon bond

MSC classification

Secondary: 60J75: Jump processes 44A10: Laplace transform
Type
Research Article
Information
Journal of Applied Probability , Volume 48 , Issue 2 , June 2011 , pp. 404 - 419
Copyright
Copyright © Applied Probability Trust 2011 

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