For Year 1 and 4.5% my Price is ( (5+(0.5*98.71+0.5*99.99))/(1+.045027)) = 99.85. What am I doing wrong?
Also for year three why have they discounted 103.94 and not the coupon payment of 105?
I ahv realized that for floor and capped bond they normally take the forward rate and add it to 100 (100+3.94) during the last year. Not sure about the logic. But in other scenario its normally 100+ coupon.
It’s a floating rate bond set in arrears where coupon is capped (i.e., not fixed) to 5%, so the coupon payment at time t+1 is equal to the smaller of (1) the interest rate at time t (i.e., the previous period), and (2) 5.00%. As a result, in year 3 (for the bottom-most node), the assumed coupon payment is equal to the interest rate in year 2, i.e., 3.9404, which is smaller than 5.
So for year 1 and 4.5%, the price is ( ( 4.5027 +(0.5*98.714+0.5*99.991))/(1+.045027)) = 99.381
I’m not certain about that reading’s definition of “set in arrears”. To my mind, that should mean that the coupon rate is set at the end of the period, when it’s paid, not at the beginning of the period (which I would expect to be called, “set in advance”). I’m going to write CFA Institute about that one.