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#1




Deferred Interest Rate Swap
I'm confused as to the answer to Exercise 9.11 in the Actex Spring 2018 manual.
ZYX Corp. enters into a 4yr loan agreement which pays 400 M at time 0 and ZYX has agreed to pay interest at the 1yr spot rate and also repay 100 M of principal at the end of each of the 4 yrs. Interest rate swap covers years 2, 3 and 4. Find the swap rate for this deferred amortizing swap. On the date of the loan, the yield curve is as follow: Years to Maturity: Spot Rate 1: 6% 2: 6.5% 3: 7% 4: 7.25% Letting P_i be the iyr PV factor P_1: .9434, P_2: .88166, P_3: .81630, P_4: .75581 and Q_j be the notional amt during the jth settlement period (in mills) Q_2: 3, Q_3: 2, Q_4: 1 I did R = [ Q_2 * (P_1  P_2) + Q_3 * (P_2  P_3) + Q_4 * (P_3  P_4) ] / [ Q_2 * P_2 + Q_3 * P_3 + Q_4 * P_4 ] = .07476309 However, the answer in the book is .074786 I also tried it with the notional amounts going from 4, 3, 2 but that didn't give me the correct answer either. I'm not sure what I'm missing here? Is it just a negligible rounding error? 
#2




I initially thought you left out year 1 by mistake, but I guess you're treating year 1 separately and years 24 as an amortizing swap. Mebbe I'll give this a go in Excel.
Are the spot rates effective annual or nominal semiannual?
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"I'm tryin' to think, but nuthin' happens!" Last edited by Breadmaker; 05042018 at 08:55 PM.. 
#3




Okay thanks! Yes maybe I didn’t mention it before but it’s 1 yr deferred swap. It doesn’t specify in the question but I believe they’re effective annual.
I pretty much just used the template the book used in previous questions just changing the notional amounts. 
#4




I did some work in Excel and got 7.74786 as the swap rate. The key thing is that the rate for yr 1 is 6%, followed by 7.74786% for years 24. You do have to take into account the CF at time 1 when doing the actuarial equivalence. This is with no rounding anywhere in the PV factors.
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#6




You have to account for the cash flow at time 1: otherwise, your pv factors and cash flows will not line up. If you include it in your formula, it should all work out.
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