2
$\begingroup$

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):

$DF(t;T)=\frac{1}{1+r(t;t,T)\cdot\alpha\left(t;t,T\right)}$

Or shall I use equation (2):

$DF(t;T)=\frac{1}{\left(1+r\left(t;t,T\right)\right)^{\alpha(t;t,T)}}$

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.

Improve this question
$\endgroup$
2
  • $\begingroup$ 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? $\endgroup$
    – Attack68 ♦
    Aug 25, 2018 at 21:52
  • $\begingroup$ 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 $\endgroup$
    – SciPhy
    Aug 26, 2018 at 8:02

3 Answers 3

Reset to default
2
$\begingroup$

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.

Improve this answer
$\endgroup$
0
$\begingroup$

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 $\frac{Act}{365}$.

My suggestion is to stick to the convention of the Libor you’ve used i.e. likely linear $\frac{Act}{365}$.

Improve this answer
$\endgroup$
0
0
$\begingroup$

following is the formula to get the Zero Rates from bootstrapped DF-

= -LN (DF) / Alpha

Where Alpha is the Accrual period

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.