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BlackDermanToy tree model question
I have a question for BDT tree.
The question is from ASM practice exam 4 #27 (p.519) #27 You are given the following BlackDermanToy tree with effective annual interest rates: Year 0........Year 1............Year 2 .............................../.....r(uu) .......... / ....6.351%...\ 5%.................................5.939% ...........\.....5.200%... / ................................\.....r(dd) A 3year cap of 6% on a notional loan amount of $1000 costs $4.80. Determine r(uu). Anyone help? I cannot understand the solution that manual provides. Other better ways? Last edited by Peter T.W. Chen; 01062018 at 11:18 AM.. 
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From the chart you can see the cap will only pay at nodes ru and ruu.
At ru cap pays: (.06315.06)/(1.06315) At ruu cap pays: (ruu.06)/(1+ruu) Add in probabilities at each node At ru: (.5)*[(.06315.06)/(1.06315)] At ruu:[(.5)(.5)]*[(ruu.06)/(1+ruu)] Discounting payoffs at these nodes leaves: At ru: (.5)*[(.06315.06)/(1.06315)] * [1/1.05] = .001410902 At ruu:[(.5)(.5)]*[(ruu.06)/(1+ruu)] *[1/1.06315]* [1/1.05] = .22395263* [(ruu.06)/(1+ruu)] We know the value of this cap is 4.80 The notional amt is 1000 Therefore: 4.80/1000 = .001410902 + .22395263* [(ruu.06)/(1+ruu)] < sum of the two discounted caps. .0048 = .001410902 + .22395263* [(ruu.06)/(1+ruu)] .01513302 = [(ruu.06)/(1+ruu)] .01513302(1+ruu) = ruu .06 .075133102 = 1.01513302 ruu ruu = .074 Overall: 1. Note where cap pays off 2. Find value of caps at their node 3. Add in the probabilities 4. Discount 5. Set equal to the cost This is my best guess! I haven't passed the exam yet though so don't take my word for it! Last edited by BartimaeusOfUruk; 01112018 at 12:35 PM.. 
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asm 10, mfe asm manual 
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