I'm using a binomial tree to price a bond that has an embedded call or put option.
On every node that has a coupon payment, do you include the coupon payment then max/min out the value, or do you max/min out the value then apply the coupon?
My guess is that for a call option, the issuer will make sure the value to the lender doesn't go beyond the call price, so we include the coupon, THEN min it out. But for a put option, the lender will make sure the value doesn't go beyond the put price, so we exclude the coupon, max the price out, THEN apply the coupon.
Is this correct?
Effectively, that's sort of like saying: assuming a continuously exercisable option, try to exercise the option 1 sliver of time before getting the coupon, then try to exercise it again 1 sliver of time after getting the coupon.