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Choosing Among Forward Rate Agreements for Yield Curve Construction

Article Quant Q&A · Author: mStudent
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Summary

The document asks how to choose between forward rate agreements that imply the same final maturity when bootstrapping a zero-coupon discount factor. It presents the discount-factor relation linking the earlier curve point, the forward rate, the accrual fraction, and the later discount factor. Two euro FRA examples use different start dates and corresponding earlier curve inputs, producing notably different estimates for the same maturity.

The question seeks a rational selection rule, but no answer or validation is included. The examples illustrate that the inputs are not interchangeable without considering quote quality, instrument conventions, liquidity, and consistency with the rest of the curve. The document does not provide evidence for choosing either contract, nor does it specify a curve-fitting or reconciliation method for handling conflicting market quotes.

Key ideas

  • An FRA quote can be used with an earlier discount factor to derive a later discount factor.
  • Different FRAs ending at the same maturity can imply different discount factors.
  • Choosing an input requires attention to quote reliability, liquidity, and contract conventions.
  • The document poses the selection problem but does not supply a resolution.

Tags

Fixed incomeStatistics
Full text
# How to select one FRA among many having the same time to maturity (Yield Curve Construction)


# How to select one FRA among many having the same time to maturity (Yield Curve Construction)












This question is related to Yield Curve Construction. I am using the old method described in this article. For the second region of the yield curve (page 8), FRAs are used. The zero-coupon yield can be computed using equation 28, from which one can derive :

$$ D(t,T_2) = \frac{D(t,T_1) }{1+\delta(T_1,T_2)F(t;T_1,T_2)}$$

The thing is that there exist on the market several FRAs with the same time to maturity (T_2 in the equation).

Example : There are 2 FRAs with time to maturity = 4M. Both can be used to compute D(t,T_2) in the above equation.

We can set $T_1 = 1M$. We have for example $D(t,T_1) = 0.178552765$. Computing $D(t,T_2)$ with FRA "EUR1X4F" (starting in 1 month, maturing 3 months later), leads to $D(t,T_2)$ = 0.174110794. If we rather set $T_1= 3M$, we have $D(t,T_1)=0.125566588$ (3M Euribor Rate). Using FRA "EUR3X4F" and the same logic, we have $D(t,T_2) = 0.124507761$.

Which FRA should we choose here? Is there any rational method for that?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.