Pricing the convertible bonds under complex call trigger condition with Longstaff and Schwartz Model

This article presents a method to price the convertible bonds under complex call trigger condition, where the issuer can only call the convertible bonds if the underlying stock price exceeds a certain level for a pre-defined number of days in a pre-defined period. Because of the path-dependent feature of the trigger condition, we employ the Longstaff and Schwartz Model, which is based on the Monte Carlo simulation. And this approach inherits the advantage of the Longstaff and Schwartz Model, which is intuitive, accurate, and computational efficient. We have also done some numerical test to show the impact of the condition and the dependence of the convertible price on the major factors.