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I am interested in Relative Value Trading of American style options on futures and have not found a whole lot of literature on it. The best resource I have discovered so far is a few pages in Colin Bennett's Trading Volatility, which is about equities. He mentions 3 methods: Theta Weighted, Vega-weighted, and dollar gamma-weighted. However no workable examples.

For 2 American options of the same expiry, but different underlying futures contracts which may be in different currencies. How would you go about determining the hedging ratio between the two legs of a spread?

For example: If A has higher implied vol then B on a similar underlying (a commodity future in different currencies), I would like to short A's Volatility and Long B's Volatility. Lets assume we are using ATM straddles. For every 1 contract of A I want to be short, i should buy X contracts of B.

What is X?

Can I have any worked examples of the Theta/Vega/Dollar Gamma type weightings?

Point me to any papers or other resources regarding this topic. Everything is appreciated. Thank you

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