Estimating the Daily Move of a Two-Futures Spread
Summary
The document asks how to estimate the expected one-day move of a spread between two futures contracts using their prices, implied volatilities, and correlation. One answer first estimates each contract’s daily move by scaling price times implied volatility by the square root of the number of trading days in a year. It then combines those moves as the square root of the sum of their variances minus twice their covariance, using correlation to account for co-movement.
This is a variance calculation for the difference between two price changes, so it can be used even when the spread’s price is negative. The exchange does not work through the supplied inputs or clarify contract units, weighting, or whether the desired spread is a price difference or a volatility spread. A second answer notes that distinction but gives no resolution; its stated subtraction of the two implied volatilities is not a calculation of spread volatility.
Key ideas
- Estimate each future’s daily price move from price, implied volatility, and the daily time scale.
- Combine the two move estimates using their correlation to calculate the spread’s standard deviation.
- For a difference of two moves, covariance enters with a negative sign.
- The exchange leaves contract weighting and the distinction between price spread and volatility spread unresolved.
Tags
Full text
# How to calculate the implied daily move of a spread between two futures contracts?
# How to calculate the implied daily move of a spread between two futures contracts?
- For a single future contract, I can calc the expected daily move (or rent) by using the following formula: ` Rent = [Future Price * Implied Volatility / SQRT (252)] `
```
Rent = [Future Price * Implied Volatility / SQRT (252)]
```
I am looking for doing the same thing for the daily expected move of a spread between two futures contract (a spread can be negative which makes the exercise harder)
Input I have are:
```
Future 1 Price = 66.50 ; Future 2 = 67.00
Implied Future 1 = 0.23 ; Implied Future 2 = 0.22
Correlation Future 1/Future 2 = 0.9850
```
Thank you for your help.
I am looking for calculating the expected move (rent) of the the spread b/w the two Fut (using the IV of the spread b/w the two Fut). Thank you for your help.
## Answer by dm63 (score 1)
https://quant.stackexchange.com/a/30680
First calculate Rent1 and Rent2 for the two futures. Then the expected daily move of the spread between the futures is
Sqrt( Rent1^2 + Rent2^2 -2Rent1Rent2Rho)
Where Rho= the correlation between daily moves ifvyhdvteonfurures
## Answer by Qen BirQeni (score 0)
https://quant.stackexchange.com/a/30239
- For the daily move you should take the square root of a single day: $$\text{Rent} = \text{Future Price}\times \text{Implied Volatility }\times \sqrt{\frac{1}{252}}$$
- $$\text{Spread} = \text{Fut1IV} - \text{Fut2IV} $$
Regarding your question, are you wanting to calculate the spread between the two Fut IV or the IV of the spread b/w the two Fut?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.