Just want to confirm when valuing calls/puts on fixed coupons and interest rates caps/floors using a binomial trees, are these all paid in arrears – one period after expiration?
If valuing 2 year call/put, cap/floor = would need to value out to 2 years using binomial tree, Today => 1 Year => 2 Years?
If valuing 1 year call/put, cap/floor = would need to value out to 1 years, Today => 1 Year => 2 Years?
Just want to see if I can wrap my head around these correctly. Is the above as everyone else understands these?
Kind of. You are correct on the cap/floors. You have to find the payoff at node 2 (year 2) and then discount by the current rate at node 2 because it is paid in arrears. That is the value of the payoff at node 2 (ie t=2).
The options on a bond is a bit different. You must calculate the value of the bond at each node using backward induction and then decide if the call/put would be exercised. If so you would own the bond at that node at the strike price - thus the payoff at that specific node doesnt need to be discounted in the same way the floor per say. However if you are valuing the option as of today then yes you would have to discount these payoffs back to today (ie discount the payoff from t=2 to today)… Same goes for floor/caps if you are trying to value them as of today (discount the payoff from above at t=2 back to today).
For calls/puts you need to figure out the size and probability of up and down moves, because the probability of the moves is NOT 50% like with bonds. From there you figure at the end of the tree if the option has value and discount it back based on probabilities and the rate at the node. Do a couple examples, it takes a little time but isn’t too difficult.