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A double obstacle model for pricing bi-leg defaultable interest rate swaps

Part of: Mathematical economics Mathematical finance Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  04 September 2019

XINFU CHEN  and
JIN LIANG Open the ORCID record for JIN LIANG [Opens in a new window]
XINFU CHEN
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, USA School of Mathematical Science, Tongji University, Shanghai, P. R. China emails: xinfu@pitt.edu; liang_jin@tongji.edu.cn
JIN LIANG
Affiliation:
School of Mathematical Science, Tongji University, Shanghai, P. R. China emails: xinfu@pitt.edu; liang_jin@tongji.edu.cn
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Abstract

Two mathematical models under so-called intensity and structure frameworks to pricing a double defaultable interest rate swap are established. The default could happen or jump to a high probability in both fixed and floating parties on the predetermined boundaries. The models lead to a new and interesting mathematical problem. As the intensity approaches infinity in designated regions, the solutions of the intensity models converge to a solution of a structure-type model which is an initial value problem of a partial differential equation coupled with two obstacles problem in their restricted regions. According to the value of the fixed rate, three cases are discussed. The free boundary that determines the swap rate and the free boundaries that determine the earlier termination of the contract (due to counterparty’s default) are analysed.

Keywords

Free boundarydouble obstacle variational inequalityinterest rate swapbi-leg defaultablestructure and intensity model

MSC classification

Primary: 35R35: Free boundary problems
Secondary: 91B25: Asset pricing models 91G70: Statistical methods, econometrics
Type
Papers
Information
European Journal of Applied Mathematics , Volume 31 , Issue 3 , June 2020 , pp. 511 - 543
Copyright
© Cambridge University Press 2019

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Footnotes

†

Chen thanks the support from the National Science Foundation Grant DMS-1516344; Liang thanks the support from the National Natural Science Foundation of China (No. 11671301).

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