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I am trying to calculate the value of an option whose underlying is the calendar spread between two months for a commodity (front month Brent vs 2nd month), usually known as a calendar spread option.

I am avoiding a CSO model as I do not know where to find implied correlation marks. However, when using the BS model I am running into issues as this spread can be negative when the market is in contango, or zero.

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You could just consider the calendar spread as a single variable. Depending on the commodity you might be able to convince yourself that it is approximated well by a normal distribution, in which case you can estimate the dollar standard deviation from historical data and then you have a simple Bachelier type modeling problem.

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There are essentially two analytical models for pricing spread options: i) the Margrabe model for the exchange of two assets (i.e. an option on the spread with strike zero), ii) the Kirk model for options on spreads with non-zero strike.

For both of them, you will need to specify a correlation coefficient $\rho$. Using BS is not possible, since it does not allow for negative prices, which is possible in spread options. Furthermore, commodity price spreads will be distributed in a significantly non-lognormal fashion, which any BS-type model is not able to capture.

Where there are no prices to infer implied correlations, I usually look at how historical correlations evolved over time. Depending on whether bid or ask prices need to be determined, i will use levels at the high or low end of the range. Hope that helps...

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