Pricing Chinese Convertible Bonds with Default Intensity by Monte Carlo Method

Xin Luo,Jinlin Zhang

doi:10.1155/2019/8610126

Abstract

This article proposes a new way to price Chinese convertible bonds by the Longstaff-Schwartz Least Squares Monte Carlo simulation. The default intensity and the volatility are the two important parameters, which are difficultly obtained in the emerging market, in pricing convertible bonds. By developing the Merton theory, we find a new effective method to get the theoretical value of the two parameters. In the pricing method, the default risk is described by the default intensity, and a default on a bond is triggered by the bottom Q(T) (default probability) percentile of the simulated stock prices at the maturity date. In the present simulation, a risk-free interest rate is used to discount the cash flows. So, the new pricing model is considered to tally with the general pricing rule under martingale measure. The empirical results of the CEB and the XIG convertible bonds by the proposed method are compared with those obtained by the credit spreads method. It is also found that the theoretical prices calculated by the method proposed in the article fit the market prices well, especially, in the long run tendency.

Highlights

Convertible bonds are highly hybrid financial derivatives, which can be converted into the issuer’s stock under some specified conditions
Ayache et al [14] applied the DI method to price convertible bonds; they used the default intensity to represent the risky interest rate; the convertible bond value can be gotten by solving the B-S partial differential equation, in which the defaultadjusted interest rate was contained, subject to the boundary conditions determined by the indenture of the convertible bond
The second section discusses the convertible bond pricing model, in which we focus on dealing with the default risk and getting the default intensity and the long-term average volatility of the underlying stock price after issuing convertible bonds

Summary

Introduction

Convertible bonds are highly hybrid financial derivatives, which can be converted into the issuer’s stock under some specified conditions. Ayache et al [14] applied the DI method to price convertible bonds; they used the default intensity to represent the risky interest rate; the convertible bond value can be gotten by solving the B-S partial differential equation, in which the defaultadjusted interest rate was contained, subject to the boundary conditions determined by the indenture of the convertible bond. The second section discusses the convertible bond pricing model, in which we focus on dealing with the default risk and getting the default intensity and the long-term average volatility of the underlying stock price after issuing convertible bonds.

The Chinese Convertible Bond Pricing Model and the Parameters Estimation

Simulation Design

The Empirical Research

Conclusion

Findings

Conflicts of Interest