Interpolating Constant-Maturity Futures Prices
Summary
The document describes constructing a synthetic futures price at a target maturity by linearly interpolating between two listed contracts whose expiries fall on either side of that target. The weights depend on how far the target lies between the shorter and longer maturities. This produces a constant-maturity series from contracts with changing expiration dates.
The response recommends expressing maturities as fractions of a year under a consistent day-count convention, with ACT/365 given as an example. It characterizes the approach as crude: it does not account for financial assumptions or market-specific features such as seasonality or events that affect a particular tenor. The document says the appropriate data frequency depends on the application; daily closing observations may suit risk-management nodes, while other uses can call for more frequent data. It does not provide empirical validation or a detailed contract-roll schedule.
Key ideas
- A target-maturity futures price can be estimated by linear interpolation between contracts bracketing that maturity.
- Interpolation weights reflect the relative distance from the target maturity to each contract expiry.
- Maturity should be expressed using a consistent day-count convention.
- The method ignores market-specific features such as seasonality or known events at particular tenors.
- Data frequency depends on the intended use, with daily observations suggested for risk-management nodes.
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Full text
# Constant maturity futures price methodology
# Constant maturity futures price methodology
What is the correct methodology to compute constant maturity futures price.
I've met in some papers that do the following. To create constant maturity synthetic futures prices with maturity $m = 30, 60,...,180$ days. We should take a pair of futures that straddle the chosen maturity $m$ with maturities $s<m<l$ measured in days until expiration.
Then the price is derived using the following formula: $$ p_m = \alpha p_s + (1-\alpha)p_l,\, \alpha = \frac{l-m}{l-s}$$
- Should the maturity be rounded to days?
- What happens when shorter futures comes closer to expiration. On which date and how we roll over the pair? Is it recommended to roll over futures several days before expiration. In this case we should have negative $\alpha$.
- What are the limitations of this methodology? What are general assumptions?
- We can take only daily closing prices or we can use more frequent data?
## Answer by UmaN (score 2)
https://quant.stackexchange.com/a/23258
What you are doing in the formula is just linear interpolation. This is probably fine, if there was some hindrance such as a seasonality effect, the market would probably contain a contract at that tenor.
- Just convert to fractions of a year by some day count convention. Say ACT/365
- I don't see why. The futures price should just approach the spot.
- It it is very crude, and does not take any financial assumptions or market specific characteristics into consideration. Limitation would be if there's nothing traded at 4.3M but every institution in the world knows that something significant happens at that time which they account for, but which you completely ignore in your simple interpolation.
- Use any frequency you like. Depends on your application. For risk management purposes, probably you are looking at daily data and create daily closing prices of your constant maturity futures nodes.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.