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Pricing of Multi-Defaultable Bonds with a Two-Correlated-Factor Hull-White Model

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  • Leonard Tchuindjo

Abstract

This research attempts to propose closed-form solutions for prices of credit-risky bonds, assuming a nonzero correlation between interest rates and credit spreads. The times of default of a credit-risky bond are modelled as the jump times of a Cox process, following the method of Lando, with an intensity that follows a Hull and White model, correlated with a similar model of the risk-free interest rate. Under the fractional recovery of market value assumption of Duffie and Singleton, the partial differential equation (PDE) for the price of the zero-coupon credit-risky bond is derived. Then this PDE is analytically solved, using the method of separation of variables, and easy-to-implement closed-form solutions are found. Finally, numerical examples are presented to show how these closed-form solutions can identify the magnitude and the direction of the credit-risky bond mispricing under different parameter assumptions.

Suggested Citation

  • Leonard Tchuindjo, 2007. "Pricing of Multi-Defaultable Bonds with a Two-Correlated-Factor Hull-White Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 19-39.
    • Handle: RePEc:taf:apmtfi:v:14:y:2007:i:1:p:19-39
    DOI: 10.1080/13504860600658943
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    References listed on IDEAS

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    1. Son-Nan Chen & Pao-Peng Hsu & Chang-Yi Li, 2016. "Pricing credit-risky bonds and spread options modelling credit-spread term structures with two-dimensional Markov-modulated jump-diffusion," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 573-592, April.
    2. Puneet Pasricha & Dharmaraja Selvamuthu & Selvaraju Natarajan, 2022. "A contagion process with self-exciting jumps in credit risk applications," Papers 2202.12946, arXiv.org.

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