# Synthesize a futures spread option

Is it possible to synthesize a futures spread option using only the options on the spread's underlyings? If so, how? If not, is there another way?

As an example, please show me how to synthesize NYMEX's RBOB Gasoline Crack Spread Options.

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This spread can't be statically synthesized. However you can synthesize it dynamically by trading in the underlying contracts. You would first value the option using standard theory (this involves solving a two-dimensional PDE, or using Monte Carlo) to get a price $V(F_1,F_2)$ in terms of the prices of the underlying futures contracts. Then the holdings in each of the underlyings are given by the deltas
$$\Delta_1 = \frac{\partial V}{\partial F_1}$$
$$\Delta_2 = \frac{\partial V}{\partial F_2}$$