In my email from a customer today (response to forum b/c sometimes it can be helpful to others)
Question:
"I have a doubt on page 41/192 of market risk material uploaded by you. The doubt relates to:
Value a plain vanilla interest rate swap based on a sequence of forward rate agreements (FRAs)
Here after calculating the forward rate we are getting 10.75% (say) and with this forward rate we are using the following formula to obtain 11.04%
2[(e10.75%*6/12)-1] =11.04%
Please clarify as to why this formula is being used. Also please intimate the possible date of uploading Credit Risk Material so that I can schedule my study program accordingly.
Answer:
Fabulous observation. I just want to remind that I YELLOW HIGHLIGHTED the Four page EdigGrid Spreadsheets that collect John Hull's interest rate and currency swaps. Why are these worth your time? Related to the question here, the analysis of a swap utilizes (gives practice to) several testable concepts. This swap-as-FRA is but a few building blocks combined.
http://learn.bionicturtle.com/images/forum/hull_swap_fra_1.png
First, make sure you can get the 10.75% forward rate from the two spot rates: 10% @ 0.25 and 10.5% @ 0.75 years.
Hull does this with CONTINUOUS COMPOUNDING:
(10.75% = 0.75*10.5% - 10%*0.25)/(0.75-0.25) = 10.75% Forward
Okay, but how can we be sure? we check to see if it works (I do this every time, i am never sure if it's right):
EXP(0.25*10%)*EXP(0.5*10.75%)=EXP(0.75*10.5%)
same as:
e^(0.25*10%)*e^(0.5*10.75%)=e^(0.75*10.5%)
Must know this. See why continuous is so elegant: it can simply be added!
Linda Allen calls this TIME CONSISTENCY and cites this as a reason for favoring continuous compounding: returns can be added. e.g., year 1 return @ 3% + year 2 return @ 6% means that 2-year = 9% under continuous.
Also note: Tuckman, however, uses semi-annual compounding. But same principle at work.
Can you solve for the forward (.25,.75) under semi-annual compounding instead, per Tuckman?
(answer will be very near to 10.75% anyway)
Second, Hull converts the continousyly rate to a semi-annual compounded rate with:
11.04% semi-annual compound freq = 2*(EXP(10.75% continuous/2)-1)
Why?
First, b/c in FRAs Hull matches compound frequency to the length (T2 - T1), in this case (0.75,0.25) = six months.
Second, more easily, it matches the 10.2% LIBOR which is a six month rate (i.e., 10.2% with semi-annual compounding)
But, IMO, this is not critical. For the question could be crafted to use continuously throughout, or to use semi-annual compounding throughout. This is sort of based on the question setup. More important to see how to do the translation.
"Also please intimate the possible date of uploading Credit Risk Material so that I can schedule my study program accordingly"
This week they will upload.
David
Question:
"I have a doubt on page 41/192 of market risk material uploaded by you. The doubt relates to:
Value a plain vanilla interest rate swap based on a sequence of forward rate agreements (FRAs)
Here after calculating the forward rate we are getting 10.75% (say) and with this forward rate we are using the following formula to obtain 11.04%
2[(e10.75%*6/12)-1] =11.04%
Please clarify as to why this formula is being used. Also please intimate the possible date of uploading Credit Risk Material so that I can schedule my study program accordingly.
Answer:
Fabulous observation. I just want to remind that I YELLOW HIGHLIGHTED the Four page EdigGrid Spreadsheets that collect John Hull's interest rate and currency swaps. Why are these worth your time? Related to the question here, the analysis of a swap utilizes (gives practice to) several testable concepts. This swap-as-FRA is but a few building blocks combined.
http://learn.bionicturtle.com/images/forum/hull_swap_fra_1.png
First, make sure you can get the 10.75% forward rate from the two spot rates: 10% @ 0.25 and 10.5% @ 0.75 years.
Hull does this with CONTINUOUS COMPOUNDING:
(10.75% = 0.75*10.5% - 10%*0.25)/(0.75-0.25) = 10.75% Forward
Okay, but how can we be sure? we check to see if it works (I do this every time, i am never sure if it's right):
EXP(0.25*10%)*EXP(0.5*10.75%)=EXP(0.75*10.5%)
same as:
e^(0.25*10%)*e^(0.5*10.75%)=e^(0.75*10.5%)
Must know this. See why continuous is so elegant: it can simply be added!
Linda Allen calls this TIME CONSISTENCY and cites this as a reason for favoring continuous compounding: returns can be added. e.g., year 1 return @ 3% + year 2 return @ 6% means that 2-year = 9% under continuous.
Also note: Tuckman, however, uses semi-annual compounding. But same principle at work.
Can you solve for the forward (.25,.75) under semi-annual compounding instead, per Tuckman?
(answer will be very near to 10.75% anyway)
Second, Hull converts the continousyly rate to a semi-annual compounded rate with:
11.04% semi-annual compound freq = 2*(EXP(10.75% continuous/2)-1)
Why?
First, b/c in FRAs Hull matches compound frequency to the length (T2 - T1), in this case (0.75,0.25) = six months.
Second, more easily, it matches the 10.2% LIBOR which is a six month rate (i.e., 10.2% with semi-annual compounding)
But, IMO, this is not critical. For the question could be crafted to use continuously throughout, or to use semi-annual compounding throughout. This is sort of based on the question setup. More important to see how to do the translation.
"Also please intimate the possible date of uploading Credit Risk Material so that I can schedule my study program accordingly"
This week they will upload.
David
