clarifying question P1.T3.175

[Jo_]

As i have insufficient rights to post in the original practice question thread (https://forum.bionicturtle.com/threads/l1-t3-174-interest-rate-swap-mechanics.4577/), i have created a new thread here.

I have a question regarding interest rate swap valuation. I understand the logic and am able to do the calculations, however i do not understand how the payment periods are determined.

E.g.: exercise 175.1: why are the cashflows after 3 months and 9 months? (6 month interval starting after 3 months)
E.g.: exercise 175.2: why are the payments after 2 months, 8 months and 14 months? (6 month interval starting after 2 months)

Probably quite a trivial reasoning, but it's keeping me from completing the rest of the exercise which is straightforward. Clarification would be most helpful!

Kr,

Joeri

 

[Alex_1]

Hi @JoeriG , my take-away from swap valuation was that one should start "backwards" when determining the payment periods.

I.e. for 175.1 we have semi-annual cash flows being exchanged and a remaining life of 9 months (additionally the text indicates 3- and 9-month LIBOR (!)). So you would start from 9 months and subtract one year and there you have the payment periods [@ 3m and @ 9m]
For 175.2 we also have semi-annual cash flows being exchanged but this time a remaining life of 14 months. This means you have payments at 14m, 8m (14-6) and 2m (8-6).

I hope this is not just a coincidence, this is just how I understood it.

Best regards,
Alex

 

[Jo_]

Hi Alex,

That actually does make sense, as your reasoning would then be that the final payment is on the final day and the payment period is six-monthly, both of which seem quite reasonable indeed

Thanks!

 

[Nicole Seaman]

@JoeriG,

I am sorry that you were having issues posting in the forum. I checked your account and there was a small error in your forum permissions that needed to be fixed. Please let me know if you are still having forum issues.

Thank you,

Nicole

 

[David Harper CFA FRM]

Hi @JoeriG It is true that, for example, a swap question is likely to omit the time to next payment if it gives the swap's life (aka, term or tenor) and the settlement frequency. @Alex_1's approach makes perfect sense; if you want the geek-math equivalent, you just need to find (solve for) the MOD operation; this wikipedia is overkill to me http://en.wikipedia.org/wiki/Modulo_operation

For example, 12 mod 5 is 2 because 5 divides into 12 twice but with a remainder (mod) of 2. So for example here are two Hull questions:

• Problem 7.3: A $100 million interest rate swap has a remaining life of 10 months. Under the terms of the swap, six-month LIBOR is exchanged for 7% per annum (compounded semiannually
• Problem 7.5: A currency swap has a remaining life of 15 months. It involves exchanging interest at 10% on £20 million for interest at 6% on $30 million once a year

In 7.3, the question requires us to realize that the next payment occurs in 10 mod 6 = 4 months.
In 7.5, the next payment occurs in 15 mod 12 = 3 months. I love simple math

 

[Jo_]

Thanks David, does make sense. Would have been a shame to miss out on a more complex question because i would have missed this straightforward first step.

Makes me think of the random number generator section somewhere, which also, to my opinion, had overkill mathematical formulas to express a simple mod operation.

Jo

PS: forum rights seem to be fixed now, as i can post in the original thread. Thanks Nicole (feel free to merge this thread into the original one if that's easier to keep track of questions).

 

[David Harper CFA FRM]

Hi @JoeriG Great! Thank you for looping back to confirm forum access: this helps us to identify the bug that occasionally causes this (we seem to have the fix, so we will be able to give XenForo the information which should allow us to squash this irritation). Thanks,