Valuation model for Chinese convertible bonds with soft call/put provision under the hybrid willow tree

Abstract

The Chinese convertible bond market has been developing rapidly in the last 10 years. However, some special characteristics of the Chinese convertible bond, such as the soft call/put provision, cause huge difficulty in the valuation. In this paper, we establish a new valuation model for the Chinese convertible bond, based on the available Chinese market data, through a hybrid willow tree approach with consideration of the underlying stock price, stochastic interest rate, and credit risk of the issuer. We employ the Brownian bridge to handle the special characteristics. Finally, we examine our model prices for the daily market closing prices for 20 Chinese convertible bonds traded from 2007 to 2017. The empirical results show the effectiveness of our valuation model under the historical and implied volatilities of the underlying stock price.

Keywords:

• Chinese convertible bond
• Default risk
• Stochastic interest rate
• Soft call/put provision
• Brownian bridge
• Willow tree approach

Acknowledgments

Finally all authors would like to express their sincere thanks to two anonymous referees for their comments and suggestions which led to making the current version of this paper readable.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The second author is supported by the Natural Sciences and Engineering Research Council of Canada (RGPIN-2020-04686) and National Natural Science Fund of China (No. U181140002).