# The pricing of perpetual convertible bond with credit risk

The pricing of perpetual convertible bond with credit risk Convertible bond gives holder the right to choose a conversion strategy to maximize the bond value, and issuer also has the right to minimize the bond value in order to maximize equity value. When there is default occurring, conversion and calling strategies are invalid. In the framework of reduced form model, we reduce the price of convertible bond to variational inequalities, and the coefficients of variational inequalities are unbounded at the original point. Then the existence and uniqueness of variational inequality are proven. Finally, we prove that the conversion area, the calling area and the holding area are connected subsets of the state space. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics-A Journal of Chinese Universities Springer Journals

# The pricing of perpetual convertible bond with credit risk

, Volume 25 (3) – Aug 25, 2010
14 pages

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Publisher
Springer Journals
Copyright © 2010 by Editorial Committee of Applied Mathematics-A Journal of Chinese Universities and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Mathematics, general
ISSN
1005-1031
eISSN
1993-0445
DOI
10.1007/s11766-010-2288-8
Publisher site
See Article on Publisher Site

### Abstract

Convertible bond gives holder the right to choose a conversion strategy to maximize the bond value, and issuer also has the right to minimize the bond value in order to maximize equity value. When there is default occurring, conversion and calling strategies are invalid. In the framework of reduced form model, we reduce the price of convertible bond to variational inequalities, and the coefficients of variational inequalities are unbounded at the original point. Then the existence and uniqueness of variational inequality are proven. Finally, we prove that the conversion area, the calling area and the holding area are connected subsets of the state space.

### Journal

Applied Mathematics-A Journal of Chinese UniversitiesSpringer Journals

Published: Aug 25, 2010

### References

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