Article

# A Valuation Model for Perpetual Convertible Bonds with Markov Regime-switching Models

Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong Pokfulam Road; Department of Mathematics and Statistics, Curtin University of Technology Perth, W.A. 6845, AUSTRALIA; Department of Finance and Management Science N. Murray Edwards School of Business, University of Saskatchewan, S7N 5A7, Saskatoon, SK, CANADA
International Journal of Pure and Applied Mathematics ————————————————————————– Volume 01/2009; 53.

ABSTRACT This paper develops a valuation model for a perpetual convert-ible bond when the price dynamics of the underlying share are governed by continuous-time Markovian regime-switching models. We suppose that the ap-preciation rate and the volatility of the underlying share are modulated by a continuous-time, finite-state, observable Markov chain. The states of this chain are interpreted as the states of an economy. Here the valuation problem of the perpetual convertible bond can be viewed as that of valuing a perpetual stock loan, or a perpetual American option with time-dependent strike price. With the presence of the regime-switching effect, the market in the model is, in gen-eral, incomplete. To provide a convenient method to determine a price kernel for valuation, we employ the regime-switching Esscher transform introduced in Elliott, Chan and Siu (2005) [4]. We then adopt the differential equation [7] to solve the optimal stopping problem associated with the valuation of the perpetual convertible bond. Numerical ex-amples are presented to illustrate the practical implementation of the proposed model.

0 0
·
0 Bookmarks
·
30 Views

Available from

### Keywords

ap-preciation rate

continuous-time Markovian regime-switching models

convenient method

differential equation

gen-eral

Numerical ex-amples

observable Markov chain

perpetual American option

perpetual convert-ible bond

perpetual convertible bond

perpetual stock loan

price dynamics

price kernel

proposed model

regime-switching effect

regime-switching Esscher

time-dependent strike price

underlying share

valuation model

valuation problem