Adjusting Bachelier Spread Option Pricing for Skew and Kurtosis

Summary

The document considers whether Bachelier’s normal model for futures spread options can be adjusted to account for nonzero skewness and excess kurtosis. The motivating case is a large transaction involving a basket of roughly twenty underlyings, where the spread is treated as approximately normal but observed distributional moments depart from normality. The author gives a skew value of -0.5 and kurtosis of 4.4.

The proposed direction is to match the distribution’s mean, standard deviation, skew, and kurtosis when valuing the spread option. However, the document asks for a reference or modified formula and provides neither a model nor pricing evidence. It also does not define the kurtosis convention or explain how the moments are estimated, limiting what can be inferred about an appropriate adjustment.

Key ideas

• The standard Bachelier spread option model assumes a normally distributed spread.
• The motivating spread exhibits skewness and kurtosis that the normal assumption does not capture.
• Moment matching is proposed as a possible way to incorporate higher distributional moments.
• No adjusted pricing formula or supporting reference is provided.

Tags

# Is there a modified Bachelier's futures spread option model with adjustments for skew and kurtosis?


# Is there a modified Bachelier's futures spread option model with adjustments for skew and kurtosis?












I'm looking at pricing a very large deal and while the distribution is kind of "normal," there's quiet a bit of skew and kurtosis that isn't being considered when I use the normal Bachelier's future spread model, which assumes the spread is normally distributed.

The skew is: -0.5, kurtosis: 4.4

So likely, someone has modified the Bachelier formula to incorporate moment matching: mean, standard deviation, skew, and kurtosis, but I can't find a reference paper on the subject. This is a huge basket of 20 underlyings or so that is roughly approximated by Bachelier's, but it's a big enough deal that people aren't comfortable if I don't moment match the distribution. Of course they wouldn't ask me to plot the distribution if I had a lognormal spread model that completely misrepresented the spread dynamics... but it is what it is.

Much appreciated!

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.