When we compare bond value to exercise price of a put or call, should we include the coupon in the same year of should we assume that the option will be exercised (if ITM) before the coupon is received? It seems to me that the coupon is not included, e.g. if a 3 year bond and we are in year 2 we calculate the present value of the bond as the coupon and principal received in year 3 and compare this with the exercise price in year 2. Hence we do not add the coupon in year 2 also to the bond value. Is that correct?
You would compare these two values in the year of exercise:
PV of the previous cash flows discounted at the current nodes rate (discount CF at t=3 up node by the t=2 rate)
Call price of the bond
You would then take the lesser of the two - lets say the bond is callable at par and the discounted value equals104. Then the bonds value assuming that rate path would be $100 + the coupon. From there you would discount back to node 1 (after of course adjusting the expected value assuming the CF’s at the t=3 down node).
In other words you include the coupon after adjusting for the put/call rules.
Assume that it is exercised on a coupon date, so the coupon is paid. You compare the strike price to the market price without the coupon (because the coupon is paid whether the option is exercised or not).
Subsequent sounds better - thanks for that.
Also to add - I’m not sure if you have ever had a bond called away from you but they do pay you the coupon (or the accrued) when doing so. That’s how I remember to always add in my coupon. For what its worth I guess.
I haven’t, but you’re correct: they pay the accrued interest. It’s a legal thing.
Yeah, that’s why I thought. So we should assume the coupon is paid before any decision is made on whether to call the bond or not?