A convertible bond is a type of hybrid security that acts like a traditional bond but includes an option to convert the bond into a predetermined number of shares of the issuing company’s stock. This feature offers investors the potential to benefit from rising stock prices while providing downside protection through regular interest payments and the return of principal upon maturity. Convertible bonds are attractive to companies as they typically pay lower interest rates than traditional bonds, making them a cost-effective way to raise capital.
Reference [1] examined the Chinese convertible bond market. The Chinese convertible bonds (CCB) have a special feature, which is a downward adjustment clause. Essentially, this clause states that when the underlying stock price remains below a pre-set level for a pre-defined number of days over the past consecutive trading days, issuers can lower the conversion price to make the conversion value higher and more attractive to investors. The authors utilized a Monte Carlo simulation approach to account for this feature and to price the convertible bond. They pointed out,
The downward adjustment provision poses a significant challenge in the pricing of CCBs. We treat the triggering of downward adjustment as a probabilistic event associated with the activation of the put option, ensuring compatibility within our pricing framework. Furthermore, we demonstrate that a unique solution exists when employing the Least Squares method to regress the continuation value at each exercise time…
In CCB research, the downward adjustment clause is often the most difficult to consider. Taking practical situations into account, in order to avoid financial distress upon put provision, bond issuers can use the downward adjustment clause to lower the conversion price. Therefore, we treat the downward adjustment clause as a probabilistic event triggering the put provision. In this way, we combine the downward adjustment clause with put provision in a simple manner.
Essentially, in this approach, the stock price is simulated, and the condition for the put provision is determined. When this condition is met, the downward adjustment works as follows,
- A probability of 0.8 is assumed for the adjustment to occur, and
- The conversion price is adjusted to the maximum of the average of the underlying stock prices over the previous 20 trading days and the last trading day.
This is another example of the versatility of the Monte Carlo approach.
Let us know what you think in the comments below or in the discussion forum.
References
[1] Yu Liu, Gongqiu Zhang, Valuation Model of Chinese Convertible Bonds Based on Monte Carlo Simulation, arXiv:2409.06496
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