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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

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

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  • $\begingroup$ Thanks that's basically what I had inferred from the paper I was reading, I appreciate the confirmation. $\endgroup$
    – Matt
    Jan 10 at 22:13

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