Option value under income and price uncertainty

We present a rigorous examination of the sign of option value under income and price uncertainty. We state and prove three theorems on the sign of option value when preferences are state independent. If income is uncertain, the sign of option value is opposite the sign of the income elasticity of the good in question. The analysis of price uncertainty is in two parts: one covers the case of own price uncertainty and the other the case where the price of some other good is uncertain. In both cases the sign of option value is generally ambiguous.