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IFoA April 2009 Q. 3 Interest Rate Swap Valuation

N

NewStudent

Active Member
I have query regarding interest rate swap valuation. I was trying to solve Q. 3) April 2009 sub-question iv)


I have following doubts in model answer paper solution:

1) How is 1/2 year interest rate arrived at ?
2)What does PV column mean?
3)What is rate and time for discount factor?
4)How are columns PV of payments & Notional calculated?


As per my understanding Value of Swap = Bfix - Bfl ; Please guide how to calculate Bfix and Bfl from question data

If any SP5 Acted Tutor guides me then it would be a great help.

Also guide me how to link images. I cannot find images attaching option in forum website. Also, my previous attachments are no longer visible (in other topics that I had started earlier)
 
Hi, this is a difficult exam question!

Taking your queries in order:

1) 1/2 year interest rate = number of days in period / 360 x annual forward interest rate

2) I think the formulae in the PV column are showing how the figures in the discount column are calculated. Eg the discount for period 3 can be arrived at using the 1/2 year forward interest rates: 1/1.0203 x 1/1.0214 x 1.0228 = 0.9382.

3) Sorry, I'm not sure what you mean here, but am hoping that my answer above resolves this?

4a) The floating payments are calculated by applying the semi-annual forward rates to the nominal value of the swap, for example, in period 1: 2.0333% x £50,000,000 = £1,016,667 . The entries in the PV of payments column are then calculated by multiplying the floating payments by the discount factors. (Note it looks as though the figures in the Examiners Report have been calculated on a spreadsheet, retaining full accuracy throughout)

4b) The Notional payments are calculated using the number of days in the period and the nominal value of the swap and then multiplying by the relevant discount factor, for example for period 1: £50,000,000 x 183/360 x 1/(1.0233333) = 24,910,160

I don't think we needed to calculate Bfix or Bfl at a point mid-way through the swap?

I'm afraid that the facility to upload images no longer works.

I hope that helps

Best wishes

Gresham
 
Thanks for the detailed explanation
Earlier I thought discount factor was (1+rate)^-period, where rate and period were values from question.
But since you explained in point no. 2 that it is product of different discount factors using different 1/2 year forward interest rates, my doubt is solved

Do you know any section in SP5 study material that helps student with such difficult questions? May be in Chapter 13?

Or do you know any sections in Hull's Textbook Options futures and other derivatives where students can find additional such difficult questions for practice?
 
Hi, I'm glad that helped

I think X Assignment question X3.3 is a good one about swaps to have a go at.

I suspect the examiners would have given credit for any reasonable approach to the April 2009 question, but Hull does give a bit more information about day count conventions if you are interested. (I have the 12th Ed of Hull and they are covered on pages 135 and 161).

Hope that helps

Gresham
 
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