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In reference to R19.P1.T3.FIN_PRODS_HULL_Ch7_Topic:Interest_Rate_Swap_Valuation:-
Hi- Happy Easter everyone ! Have a quick question on the example illustrated below which I was revisiting..

In the FRA Method of IRSwap Valuation:-
i) We calculated/extracted the "Continuous"-Forward Rates.
ii) Next we converted the "Continuous"-Forward Rates into "Discrete" Semi-Annual-Forward Rates
which makes sense because 10.2 is the discrete rate- so we convert the 9 month and the 15 month rate into discrete rates as well.
iii) Next we calculate the Floating CFs based on the "Discrete" Semi-Annual-Forward Rates.
iv) But then we calculate the Final NET CFs based on the the "Continuous"-Discount Factors !

My Question is that, if we have used the "Discrete" Semi-Annual-Forward Rates for calculating the Floating CFs, should we not have used "Discrete"-Semi-Annual-Discount Factors instead of "Continuous"-Discount Factors...?

I may be missing a crucial point here... :-( Much gratitude on any insights on this...

@David Harper CFA FRM @ShaktiRathore First off-My apologies for nudging you guys on this topic knowing it's just out of the Easter weekend ...was waiting to clear this one up and wrap up this topic...and worried that this thread might have gotten lost in the pile of threads over the weekend...so, whenever you guys get a chance, if you could share some insights on this , would be very grateful ... Last edited:

David Harper CFA FRM

David Harper CFA FRM
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HI @gargi.adhikari That's a very good question. This is Hull's example of course, but I think it's very instructive practice with respect to compound frequencies. I first think it's important here to keep in mind the difference (distinction) between the discount rate and the rates used in the swap (i.e., swap rate and LIBOR). A feature of swaps is that we cannot naturally determine the swap cash flows based on a continuous rate. So, at you have noted above, in the valuation of an IRS as FRAs both legs are necessarily using semi-annual rates to determine the cash flows.
• In this case of the fixed rate cash flow, this is easy because the fixed rate ("receive fixed") of 8.0% is already given with semi-annual compound frequency. $100*8.0%/2 =$4.00 received every six months.

Nicole Seaman

Staff member
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Even though they do not use the same example, there are other threads in the forum that can help you to understand this concept. Here are a few threads that I found with a quick search that should be helpful to you, as they discuss the last payment date:
Thank you,

Nicole

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
Hi @gargi.adhikari We are at time 0, trying to determine the immediate value of the swap with 15 months (1.25 years) remaining tenor (life). If the swap coupons exchange every six months, and the next exchange occurs in three months (+0.25 years), then the "last payment date" was three months prior (- 0.25 years). The "LIBOR at last coupon" was 10.2%; i.e., three months ago, six month LIBOR was 10.2%. The reason Hull gives this assumption is that the floating rate is observed at the beginning of the (six-month, in this case) period, but paid at the end of the (six-month) period. That's why the first floating cash flow is $5.10 = 10.2%/2 *$100. As of today (Time 0), we should already know the next floating rate payment because the floating rate was observed three months ago. Going further forward in time, to the coupon payable in nine months (0.75 years), we do NOT currently know the floating rate: it will be observed in three months. So, we estimate it by using the forward rate, F(0.25, 0.75) that is implied in the currently observed spot rate curve. I hope that helps!

Got it    Thanks so much @David Harper CFA FRM - I was missing the key insight that the floating rate is observed at the beginning of the (six-month, in this case) period, but paid at the end of the (six-month) period - that helped a lot  