# Pretty Good Practice Question...IR Calls

A two-period interest rate tree has the following expected one-period rates: t = 0 … t = 1 … t = 2 …7.12% …6.83% 6.00% …6.84% … 6.17% … 6.22% The price of a two-period European interest-rate call option on the one-period rate with a strike rate of 6.25% and a principal amount of \$100,000 is closest to: A) \$725.86. B) \$423.89. C) \$449.33. D) \$704.22.

c

C too but I am not sure about the probability, as I took 50% U and D…

C

I get B Prices …812.17 (need to discount it back at the t=2 rate, I think) …638.58 423.89…552.23 …260.07 …0

I’d go with B too…

can somebody walk me through this…

Nice job… Mumu & Wander… Your answer: B was correct! Calculate the payoffs on the call in percent for I++ and I+− (= I−+): I++ value = (0.0712 − 0.0625) / 1.0712 = 0.00812173. I+− value = (0.0684 − 0.0625) / 1.0684 = 0.00552228. Remember that the payoff on the call value is the present value of the interest rate difference based on the rate realized at t = 2 because the payment is received at t = 3. Calculate the t = 1 values (the probabilities in an interest rate tree are 50%): At t = 1 the values are I+ = [0.5(0.00812173) + 0.5 (0.00552228)] / 1.0683 = 0.00638585. At t = 1 the values are I− = [0.5(0) + 0.5 (0.00552228)] / 1.0617 = 0.00260068. Calculate the t = 0 value: At t = 0 the option value is [0.5(0.00638585) + 0.5(0.00260068)] / 1.06 = 0.00423893 0.00423893 × 100,000 = \$423.89. Dont forget to discount that last time period, in this case T=2, by that rate… otherwise you will end up getting C for an ans…

chad, don’t answer yet. give me a couple of min to calculate …

bummer, at least good to know I was on the right track.

maratikus Wrote: ------------------------------------------------------- > chad, don’t answer yet. give me a couple of min > to calculate … haha… my bad…

never mind…was trying to do a bond premium

yep, forgot to use t=2. good question. thanks for that one.

rekooh Wrote: ------------------------------------------------------- > can somebody walk me through this… t = 0 … t = 1 … t = 2 …7.12% = Value = (0.0712 - 0.0625)/1.0712 = 0.00812173 …6.83% Value = (.00812 + .00552)/2/1.0683 = 0.006386 6.00% …6.84% = Value = (0.0684 - 0.0625)/1.0684 = 0.00552228 … 6.17% Value = (0.00552 + 0 )/2/1.1617 = 0.0026007 … 6.22% = Value = 0 At point 6.00 Discount back (0.006386 + 0.0026007)/2/1.06 = 423.9

just so I am clear, if we wanted the value of the entire cap, instead of just the 2 year caplet, we would need to do the same calcs again just for the one year rates etc. and then add the two caplets together

In the Schweser example, it says you have to determine the 2-year caplet and the 1-year caplet and add them together? But we didn’t do that here. What is the difference?

Well, I now see Rekooh’s post and know that my answer.

Well, I now see Rekooh’s post and know the answer.