Pricing Chinese Convertible Bonds with Default Intensity by Monte Carlo Method

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.