Mixing
Discount Factors to Zero Rates
Clash Royale CLAN TAG#URR8PPP
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I have obtained a Ibor-6Months curve using bootstrapping techniques. For the short-term of the curve I used spot, for the middle-term FRAs and for the long-term IRS.
The curve that I have obtained is given in discount factors...(using the configuration detailed above). The question is, how can I now obtain the zero rate curve once the discount factors are known?
Shall I use equation (1):
$DF(t;T)=frac11+r(t;t,T)cdotalphaleft(t;t,Tright)$
Or shall I use equation (2):
$DF(t;T)=frac1left(1+rleft(t;t,Tright)right)^alpha(t;t,T)$
where $alpha$ refers to the year fraction and $r$ is the zero rate, $t$ is the actual time and $T$ is the maturity time.
Is the equation the same for any tenor (taking into account that the instruments involved are different)? I would say IRS tenors follow the equation (2) while spots or FRA tenors follow the equation (1).
Any comments are welcome!
Thank you very much in advance.
yield-curve discount-factor-curve
edited Aug 25 at 20:07
Alex C
5,392921
asked Aug 25 at 19:12
pistacho
511
add a comment |Â
up vote
1
down vote
favorite
I have obtained a Ibor-6Months curve using bootstrapping techniques. For the short-term of the curve I used spot, for the middle-term FRAs and for the long-term IRS.
The curve that I have obtained is given in discount factors...(using the configuration detailed above). The question is, how can I now obtain the zero rate curve once the discount factors are known?
Shall I use equation (1):
$DF(t;T)=frac11+r(t;t,T)cdotalphaleft(t;t,Tright)$
Or shall I use equation (2):
$DF(t;T)=frac1left(1+rleft(t;t,Tright)right)^alpha(t;t,T)$
where $alpha$ refers to the year fraction and $r$ is the zero rate, $t$ is the actual time and $T$ is the maturity time.
Is the equation the same for any tenor (taking into account that the instruments involved are different)? I would say IRS tenors follow the equation (2) while spots or FRA tenors follow the equation (1).
Any comments are welcome!
Thank you very much in advance.
yield-curve discount-factor-curve
edited Aug 25 at 20:07
Alex C
5,392921
asked Aug 25 at 19:12
pistacho
511
Personally I have used both depending upon the context and to be consistent with the market terminology for different products. In all honesty I have never found the zero rate to be useful for anything really, certainly not analysis wise. For what purpose are you interested in its calculation?
– Attack68
Aug 25 at 21:52
I think i got it...for a fix-float Euribor-6M IRS, we have the floating leg following semi-annually coupons while in the fixed leg we have annually coupons. This annual coupons does not appear in FRA instruments (due to the fact that both legs are semi-annually). This makes short and middle-term following Equation (1), while the long term follows Equation (2), which is annually compounded due the annual coupons on IRS
– pistacho
Aug 26 at 8:02
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I have obtained a Ibor-6Months curve using bootstrapping techniques. For the short-term of the curve I used spot, for the middle-term FRAs and for the long-term IRS.
The curve that I have obtained is given in discount factors...(using the configuration detailed above). The question is, how can I now obtain the zero rate curve once the discount factors are known?
Shall I use equation (1):
$DF(t;T)=frac11+r(t;t,T)cdotalphaleft(t;t,Tright)$
Or shall I use equation (2):
$DF(t;T)=frac1left(1+rleft(t;t,Tright)right)^alpha(t;t,T)$
where $alpha$ refers to the year fraction and $r$ is the zero rate, $t$ is the actual time and $T$ is the maturity time.
Is the equation the same for any tenor (taking into account that the instruments involved are different)? I would say IRS tenors follow the equation (2) while spots or FRA tenors follow the equation (1).
Any comments are welcome!
Thank you very much in advance.
yield-curve discount-factor-curve
edited Aug 25 at 20:07
Alex C
5,392921
asked Aug 25 at 19:12
pistacho
511
I have obtained a Ibor-6Months curve using bootstrapping techniques. For the short-term of the curve I used spot, for the middle-term FRAs and for the long-term IRS.
The curve that I have obtained is given in discount factors...(using the configuration detailed above). The question is, how can I now obtain the zero rate curve once the discount factors are known?
Shall I use equation (1):
$DF(t;T)=frac11+r(t;t,T)cdotalphaleft(t;t,Tright)$
Or shall I use equation (2):
$DF(t;T)=frac1left(1+rleft(t;t,Tright)right)^alpha(t;t,T)$
where $alpha$ refers to the year fraction and $r$ is the zero rate, $t$ is the actual time and $T$ is the maturity time.
Is the equation the same for any tenor (taking into account that the instruments involved are different)? I would say IRS tenors follow the equation (2) while spots or FRA tenors follow the equation (1).
Any comments are welcome!
Thank you very much in advance.
yield-curve discount-factor-curve
edited Aug 25 at 20:07
Alex C
5,392921
asked Aug 25 at 19:12
pistacho
511
edited Aug 25 at 20:07
Alex C
5,392921
edited Aug 25 at 20:07
Alex C
5,392921
edited Aug 25 at 20:07
Alex C
5,392921
5,392921
asked Aug 25 at 19:12
pistacho
511
asked Aug 25 at 19:12
pistacho
511
asked Aug 25 at 19:12
pistacho
511
511
Personally I have used both depending upon the context and to be consistent with the market terminology for different products. In all honesty I have never found the zero rate to be useful for anything really, certainly not analysis wise. For what purpose are you interested in its calculation?
– Attack68
Aug 25 at 21:52
I think i got it...for a fix-float Euribor-6M IRS, we have the floating leg following semi-annually coupons while in the fixed leg we have annually coupons. This annual coupons does not appear in FRA instruments (due to the fact that both legs are semi-annually). This makes short and middle-term following Equation (1), while the long term follows Equation (2), which is annually compounded due the annual coupons on IRS
– pistacho
Aug 26 at 8:02
add a comment |Â
Personally I have used both depending upon the context and to be consistent with the market terminology for different products. In all honesty I have never found the zero rate to be useful for anything really, certainly not analysis wise. For what purpose are you interested in its calculation?
– Attack68
Aug 25 at 21:52
I think i got it...for a fix-float Euribor-6M IRS, we have the floating leg following semi-annually coupons while in the fixed leg we have annually coupons. This annual coupons does not appear in FRA instruments (due to the fact that both legs are semi-annually). This makes short and middle-term following Equation (1), while the long term follows Equation (2), which is annually compounded due the annual coupons on IRS
– pistacho
Aug 26 at 8:02
Personally I have used both depending upon the context and to be consistent with the market terminology for different products. In all honesty I have never found the zero rate to be useful for anything really, certainly not analysis wise. For what purpose are you interested in its calculation?
– Attack68
Aug 25 at 21:52
Personally I have used both depending upon the context and to be consistent with the market terminology for different products. In all honesty I have never found the zero rate to be useful for anything really, certainly not analysis wise. For what purpose are you interested in its calculation?
– Attack68
Aug 25 at 21:52
I think i got it...for a fix-float Euribor-6M IRS, we have the floating leg following semi-annually coupons while in the fixed leg we have annually coupons. This annual coupons does not appear in FRA instruments (due to the fact that both legs are semi-annually). This makes short and middle-term following Equation (1), while the long term follows Equation (2), which is annually compounded due the annual coupons on IRS
– pistacho
Aug 26 at 8:02
I think i got it...for a fix-float Euribor-6M IRS, we have the floating leg following semi-annually coupons while in the fixed leg we have annually coupons. This annual coupons does not appear in FRA instruments (due to the fact that both legs are semi-annually). This makes short and middle-term following Equation (1), while the long term follows Equation (2), which is annually compounded due the annual coupons on IRS
– pistacho
Aug 26 at 8:02
add a comment |Â
2 Answers
2
active
oldest
votes
up vote
2
down vote
Equation 2 gives the annual zero rate for all tenors. In practice, people sometimes quote rates f less than one year using Equation 1, but in general , equation 2 is used.
answered Aug 25 at 22:49
dm63
6,5851624
add a comment |Â
up vote
0
down vote
You can use either but a rate and a curve are only well defined if given alongside calculation conventions.
The convention in Equation 1 is that the rate is linear, in Equation 2 it is (annually) compounded.
Moreover you need a daycount convention to calculate the year fraction between two dates, for example $fracAct365$.
My suggestion is to stick to the convention of the Libor you’ve used i.e. likely linear $fracAct365$.
answered Aug 25 at 23:18
Ivan
72647
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
Equation 2 gives the annual zero rate for all tenors. In practice, people sometimes quote rates f less than one year using Equation 1, but in general , equation 2 is used.
answered Aug 25 at 22:49
dm63
6,5851624
add a comment |Â
up vote
2
down vote
Equation 2 gives the annual zero rate for all tenors. In practice, people sometimes quote rates f less than one year using Equation 1, but in general , equation 2 is used.
answered Aug 25 at 22:49
dm63
6,5851624
add a comment |Â
up vote
2
down vote
up vote
2
down vote
Equation 2 gives the annual zero rate for all tenors. In practice, people sometimes quote rates f less than one year using Equation 1, but in general , equation 2 is used.
answered Aug 25 at 22:49
dm63
6,5851624
Equation 2 gives the annual zero rate for all tenors. In practice, people sometimes quote rates f less than one year using Equation 1, but in general , equation 2 is used.
answered Aug 25 at 22:49
dm63
6,5851624
answered Aug 25 at 22:49
dm63
6,5851624
answered Aug 25 at 22:49
dm63
6,5851624
answered Aug 25 at 22:49
dm63
6,5851624
6,5851624
add a comment |Â
add a comment |Â
up vote
0
down vote
You can use either but a rate and a curve are only well defined if given alongside calculation conventions.
The convention in Equation 1 is that the rate is linear, in Equation 2 it is (annually) compounded.
Moreover you need a daycount convention to calculate the year fraction between two dates, for example $fracAct365$.
My suggestion is to stick to the convention of the Libor you’ve used i.e. likely linear $fracAct365$.
answered Aug 25 at 23:18
Ivan
72647
add a comment |Â
up vote
0
down vote
You can use either but a rate and a curve are only well defined if given alongside calculation conventions.
The convention in Equation 1 is that the rate is linear, in Equation 2 it is (annually) compounded.
Moreover you need a daycount convention to calculate the year fraction between two dates, for example $fracAct365$.
My suggestion is to stick to the convention of the Libor you’ve used i.e. likely linear $fracAct365$.
answered Aug 25 at 23:18
Ivan
72647
add a comment |Â
up vote
0
down vote
up vote
0
down vote
You can use either but a rate and a curve are only well defined if given alongside calculation conventions.
The convention in Equation 1 is that the rate is linear, in Equation 2 it is (annually) compounded.
Moreover you need a daycount convention to calculate the year fraction between two dates, for example $fracAct365$.
My suggestion is to stick to the convention of the Libor you’ve used i.e. likely linear $fracAct365$.
answered Aug 25 at 23:18
Ivan
72647
You can use either but a rate and a curve are only well defined if given alongside calculation conventions.
The convention in Equation 1 is that the rate is linear, in Equation 2 it is (annually) compounded.
Moreover you need a daycount convention to calculate the year fraction between two dates, for example $fracAct365$.
My suggestion is to stick to the convention of the Libor you’ve used i.e. likely linear $fracAct365$.
answered Aug 25 at 23:18
Ivan
72647
answered Aug 25 at 23:18
Ivan
72647
answered Aug 25 at 23:18
Ivan
72647
answered Aug 25 at 23:18
Ivan
72647
72647
add a comment |Â
add a comment |Â
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Personally I have used both depending upon the context and to be consistent with the market terminology for different products. In all honesty I have never found the zero rate to be useful for anything really, certainly not analysis wise. For what purpose are you interested in its calculation?
– Attack68
Aug 25 at 21:52
I think i got it...for a fix-float Euribor-6M IRS, we have the floating leg following semi-annually coupons while in the fixed leg we have annually coupons. This annual coupons does not appear in FRA instruments (due to the fact that both legs are semi-annually). This makes short and middle-term following Equation (1), while the long term follows Equation (2), which is annually compounded due the annual coupons on IRS
– pistacho
Aug 26 at 8:02