# How to 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.

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

$$\Delta_1 = \frac{\partial V}{\partial F_1}$$

$$\Delta_2 = \frac{\partial V}{\partial F_2}$$

By re-adjusting your holdings at some specified frequency, you can replicate the payoff of the option.

• Thank-you! I think I understand what you're saying, but when you say "statically", do you mean that no closed form is known? I don't specialize in synthesis or this type of math, so if you'd mind showing me the explicit result, would you mind pointing me to some relevant academics? Thank you so very much in advance, and thank you for this great answer! – user6500 Nov 16 '13 at 1:35
• @user6500: It means that you cannot buy a combination of contracts and hold them from beginning to end and thereby completely hedge your option. – vonjd Dec 22 '14 at 11:03