Using the following tree of semiannual interest rates what is the value of a 5% callable bond that has one year remaining to maturity, a call price of 99 and pays coupons semiannually? t=1) 7.76% t=0) 6.20% t=1) 5.45% The answer is 98.29, but I am getting 99.06. I am getting the first nodes right (98.67 and 99), but for some reason am off on the current value…
price at t = 1 with 7.76% = min(99,102.5/(1+7.76%/2))=98.67 price at t = 1 with 5.45% = min(99,102.5/(1+5.45%/2)=99 price at t = 0: =min(99,((98.67+99)/2+2.5)/(1+6.20%/2)=92.29
prices at nodes 1 and 2 shud be Node 1 : 98.67+2.5 = 101.17 Node 2 :99+2.5 = 101.5 discount these prices with (1+6.2/200) i.e 1.031 and avg them …shud give you 98.28