Skip to content
All library documents

Annualizing Spread Volatility for the Bachelier Spread Option Model

Article Quant Q&A · Author: Matt
Read the original

Summary

The document explains how to express historical spread volatility when using the Bachelier single-factor spread option formula. Since the option’s underlying is the price difference between two futures contracts, the volatility input is measured in spread-price units rather than as a percentage return on the spread. The response clarifies that when the model’s time variable is in years, its volatility input should be annualized accordingly.

For historical estimation, the cited discussion describes calculating volatility from daily spread observations and annualizing it with the square root of 252, a convention used in commodity markets. This answers the unit question, but the document gives no worked calculation or detail about the estimation window, treatment of missing observations, or whether volatility is stable over time. It also notes that the questioner is setting aside market implied volatility, so the guidance addresses historical inputs rather than calibration to option prices.

Key ideas

  • Bachelier spread volatility is expressed in price units of the underlying spread, not as a spread return.
  • When model time is measured in years, the volatility input should be annualized.
  • Historical daily spread volatility can be annualized using the square root of 252 under the convention described.
  • The discussion does not specify an estimation window or assess the limitations of historical volatility.

Tags

OptionsFuturesCommoditiesVolatilityDerivatives pricing
Full text
# Bachelier Spread formula - input spread volatility question


# Bachelier Spread formula - input spread volatility question












I don't have much experience using Bachelier's single factor spread option formula, but I know it takes a dollar volatility of the spread as an input. What I don't know, is that just the standard deviation of the daily spread? Or is it annualized? Say for simplicity I'm using the historical data, and trying to estimate the input volatility for the model. What's the correct approach? (Yes, I'm ignoring implied vols from the market).

From what I've read (well, the only paper comparing historical vols to implied ones using Bachelier's spread), it appears it is annualized spread vol: Section F.1: The implied volatility calculation is actually determined by the price level of the futures contracts rather than the price return of the futures contracts underlying the option. This is because the underlying variable of the future spread option is the spread value between two futures contracts, so it does not make sense to interpret the volatility with respect to the return of the spread value.

Then in E.2 where they are looking at the historical daily spread, they annualize it with the simple sqrt(252) commonly used in commodity markets: http://www.sfu.ca//~poitras//Final.doc

## Answer by user59852 (score 1, accepted)

https://quant.stackexchange.com/a/69429

Normally, the "time" variable unit is years. So the volatility is normalized to be a year volatility.

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.