The current stock price is $100 and evolves in a binomial tree with two periods with 10% up moves and -5% down moves. The risk-free rate is 2% per period. Here, one period is half a year. Consider a convertible bond with 1 year to maturity. The nominal value is $100 and the bond pays an annual coupon of $5. The conversion price is $100, i.e., one bond can be converted into one share.

Assume that the coupon payment is delivered every half a year. The last coupon payment will be delivered exactly the same time with the principal payment. In addition, the investors can choose to convert the bond before the principal payment and before the last coupon payment