Credit derivatives pricing with default density term structure modelled by Lévy random fields

Lijun Bo, Ying Jiao () and Xuewei Yang
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Lijun Bo: Department of Mathematics, Xidian University - Xidian University
Ying Jiao: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon
Xuewei Yang: School of Mathematical Sciences, Nankai University - Nankai University, 94 Weijin Road, Nankai District, Tianjin 300071 China

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Abstract: We model the term structure of the forward default intensity and the default density by using Lévy random fields, which allow us to consider the credit derivatives with an after-default recovery payment. As applications, we study the pricing of a defaultable bond and represent the pricing kernel as the unique solution of a parabolic integro-differential equation. Finally, we illustrate by numerical examples the impact of the contagious jump risks on the defaultable bond price in our model.

Date: 2014-06-01
Note: View the original document on HAL open archive server: https://hal.science/hal-00651397v1
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Published in Stochastic Analysis and Applications, 2014, 32 (2), pp.229-252

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