Hi everyone I’m reading the Schweser textbook on valuing interest rate caps and am unable to unravel the example given. Where does the $333,094 come from in the question? The photo of the example is attached and there are only 2 pages. Can someone help? Thanks! PS: I will remove the link to the image after a few days just in case there are copyright issues. 
333,094 is the value of 2 year caplet whereas 233,513 is discounted back to t0 to compute the value of 1 year caplet. Value of 2 year cap=value of 1 year caplet+value of 2 year caplet.233,513 is the payoff ie diff B/W 5.99-5 *notional principal 25m discounted at the rate of 5.99,
333.094 is the value of 2 year caplet.
value in third node UU 8,56 % - cap rate (55) 0 3,56% x notional 25M = 890.000 discounted by rate in this node of 1,0599 = 819.823
value in third node UD 6,34% - 5% (cap rate) = 1,34 % x notional and discount by 1,0634 you will get 315.027
value in third node DD coupon rate is less than cap rate thus cap value is 0 in this node.
value in second node U and D - simply 0,5 of third node for U discount by rate in this node 1,0599. You will get amount of cap of 535.357
value in second node D only discount 0,5 of cap value from third node UD since cap value in third node DD is 0.
you will get cap value of 150.817
cap value in period 0 (first node) (0,5 x 535.357) + (0,5 x 150.817) /1,03 - discount by first node discount rate
and you will get 2 year caplet value of 333.094
When you calculate 1 year caplet add 2 year caplet value to 1 year caplet value to get the value of cap =
113.356 + 333.094 = 446.450
similar technique you use for discounting bonds with embedded call options. To calculate floornet the path is just opposite, you will get the value of floor whenever int. rate falls below floor strike rate.
Hi Flashback thanks that working I understand it now.
Just a few corrections, probably due to the haste in typing out the full working:
value in third node UU 8,56 % - cap rate (5.5%) 3.56% x notional 25M = 890.000 discounted by rate in this node of 1,0599 = 819.823
value in second node U and D - simply 0,5 of third node for U and 0.5 of third node centre, discount by rate in this node 1,0599. You will get amount of cap of 535.357
Thanks again!
You 're welcome. If there are any error I made an error because I solved it yesterday quickly on paper while answering with my comp calculator, not BA II Plus.