Actuarial Outpost
 
Go Back   Actuarial Outpost > Exams - Please Limit Discussion to Exam-Related Topics > SoA/CAS Preliminary Exams > Exam 2/FM - Financial Mathematics
FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions


Fill in a brief DW Simpson Registration Form
to be contacted when new jobs meet your criteria.


Reply
 
Thread Tools Search this Thread Display Modes
  #1  
Old 05-04-2018, 08:33 PM
kianalf kianalf is offline
SOA
 
Join Date: Jan 2018
College: University of California, San Diego Alumni
Posts: 6
Unhappy 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 4-yr loan agreement which pays 400 M at time 0 and ZYX has agreed to pay interest at the 1-yr 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 i-yr PV factor
P_1: .9434, P_2: .88166, P_3: .81630, P_4: .75581

and Q_j be the notional amt during the j-th 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?
Reply With Quote
  #2  
Old 05-04-2018, 08:49 PM
Breadmaker's Avatar
Breadmaker Breadmaker is offline
Member
SOA
 
Join Date: May 2009
Studying for CPD - and nuttin' else!
College: Swigmore U
Favorite beer: Guinness
Posts: 2,820
Default

I initially thought you left out year 1 by mistake, but I guess you're treating year 1 separately and years 2-4 as an amortizing swap. Mebbe I'll give this a go in Excel.

Are the spot rates effective annual or nominal semi-annual?
__________________
"I'm tryin' to think, but nuthin' happens!"

Last edited by Breadmaker; 05-04-2018 at 08:55 PM..
Reply With Quote
  #3  
Old 05-04-2018, 11:12 PM
kianalf kianalf is offline
SOA
 
Join Date: Jan 2018
College: University of California, San Diego Alumni
Posts: 6
Default

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.
Reply With Quote
  #4  
Old 05-04-2018, 11:47 PM
Breadmaker's Avatar
Breadmaker Breadmaker is offline
Member
SOA
 
Join Date: May 2009
Studying for CPD - and nuttin' else!
College: Swigmore U
Favorite beer: Guinness
Posts: 2,820
Default

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 2-4. 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.
__________________
"I'm tryin' to think, but nuthin' happens!"
Reply With Quote
  #5  
Old 05-05-2018, 12:02 AM
kianalf kianalf is offline
SOA
 
Join Date: Jan 2018
College: University of California, San Diego Alumni
Posts: 6
Default

Ah I see, I think I need to work a little harder with my calculator keystrokes as well.

Thank you!
Reply With Quote
  #6  
Old 05-05-2018, 08:55 AM
Breadmaker's Avatar
Breadmaker Breadmaker is offline
Member
SOA
 
Join Date: May 2009
Studying for CPD - and nuttin' else!
College: Swigmore U
Favorite beer: Guinness
Posts: 2,820
Default

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.
__________________
"I'm tryin' to think, but nuthin' happens!"
Reply With Quote
Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off


All times are GMT -4. The time now is 08:36 AM.


Powered by vBulletin®
Copyright ©2000 - 2018, Jelsoft Enterprises Ltd.
*PLEASE NOTE: Posts are not checked for accuracy, and do not
represent the views of the Actuarial Outpost or its sponsors.
Page generated in 0.18518 seconds with 11 queries