Anchor Dates and Settlement Lags in Yield Curve Construction
Summary
Yield curve construction depends on the date at which the discount factor is set to one. The document explains that market bond prices on a trade date generally reflect settlement on a later date, so a curve built from those prices may be anchored to settlement rather than to the trade date. It distinguishes common conventions: swap curves are often anchored to today, while government bond curves are more often anchored to the spot settlement date.
If a government curve must instead be anchored to today, the curve can be discounted back from settlement using repo rates. When discounting bond cash flows with a today-anchored curve, the observed dirty bond price must also be adjusted consistently for its settlement date. These are described as market conventions rather than universal rules; the appropriate setup should be confirmed with the relevant traders. The explanation gives no detailed bootstrapping procedure or country-by-country convention survey.
Key ideas
- A yield curve's anchor date is the date assigned a discount factor of one.
- Swap curves are commonly anchored to the trade date, while government curves often use the spot settlement date.
- Repo rates can be used to discount a settlement-anchored curve back to today.
- Bond prices and cash-flow discount factors must use consistent dates.
- Curve conventions vary, so practitioners should confirm the required setup with traders.
Tags
Full text
# Spot period considerations in yield curves
# Spot period considerations in yield curves
Textbook explanations of yield curve modelling discuss bootstrapping or other methods. If we take sovereign bonds for deriving the curve, we would get price data from a market data provider like Bloomberg.
However, the prices on a specific date $t$ are actually prices for the settlement date $t+x$ (e.g. $t+1$ or $t+2$ in some countries). Therefore, the curve that results from our model is not a spot curve, but a forward curve. How does one in practice take into consideration this time lag (spot period) for creating spot / zero-coupon curves? I could guess that one uses overnight or repo rates for additional discounting of the bonds, but I would be interested in actual market practice.
## Answer by Helin (score 3, accepted)
https://quant.stackexchange.com/a/37622
This bothered me a great deal when I started out years ago =P
In curve construction, we unofficially have the concept of an "anchor date," which is the date on which the discount factor is 1.
In swap curve construction, most market participants set the anchor date to "today" (the trade date). So a USD "spot" swap is actually a 2-day forward swap.
In government curve construction, it is actually more common to set the anchor date to the spot settlement date (e.g., $\text{today} + 1$ for the US). In cases where the anchor date does need to be today, we simply discount the curve back to today using repo, as you suggested.
If a curve is constructed using "today" as the anchor date, when it's used to discount bond cash flows, you need to be careful to discount the market bond price back to today to be consistent with your curve:
$$ (P + AI) \cdot d(\text{settlement date}) = \sum_{i=1}^n c_i \cdot d(t_i). $$
These are not hard rules at all. In practice, it's always best to consult your traders to see what they want.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.