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The valuation of convertible bonds with numeraire changes

The valuation of convertible bonds with numeraire changes The changes of numeraire can be used as a very powerful mean in pricing contingent claims in the context of a complete market. We apply the method of nurmeraire changes to evaluate convertible bonds when the instantaneous growth and variance of the value of issuer and those of zero-coupon bonds follow a general adapted stochastic process in this paper. A closed-form solution is derived when the instantaneous growth and variance of the value of issuer and those of zero-coupon bonds are deterministic function of time. We also consider a special case when the asset price follows GBM (Geometric Brownian Motion) and interest rate follows Vasicek’s model. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

The valuation of convertible bonds with numeraire changes

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Publisher
Springer Journals
Copyright
Copyright © 2010 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Theoretical, Mathematical and Computational Physics; Math Applications in Computer Science; Applications of Mathematics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-009-9042-0
Publisher site
See Article on Publisher Site

Abstract

The changes of numeraire can be used as a very powerful mean in pricing contingent claims in the context of a complete market. We apply the method of nurmeraire changes to evaluate convertible bonds when the instantaneous growth and variance of the value of issuer and those of zero-coupon bonds follow a general adapted stochastic process in this paper. A closed-form solution is derived when the instantaneous growth and variance of the value of issuer and those of zero-coupon bonds are deterministic function of time. We also consider a special case when the asset price follows GBM (Geometric Brownian Motion) and interest rate follows Vasicek’s model.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Mar 18, 2010

References