The statement that compound options have the same strike price but two expiration dates is inconsistent with the definition of compound options. Compound options, in fact, have two distinct strike prices and two distinct expiration dates. This dual structure is what gives compound options their unique characteristic of being 'options on options'. For instance, consider a call on call compound option. If the current price of the underlying asset is above the first strike price (X1) on the first exercise date (T1), the investor has the right to pay the first strike price (X1) and receive a call option. This newly acquired call option then gives the investor the right to purchase the underlying asset for the second strike price (X2) on the second exercise date (T2). Therefore, the assertion that compound options have the same strike price but two expiration dates is incorrect and inconsistent with the nature of compound options.

Choice A is incorrect. Feature I is consistent with the definition of compound options. Compound options are indeed 'options on options', providing an additional layer of optionality to the holder. This means that the holder has the right, but not the obligation, to exercise another option.

Choice C is incorrect. Feature III aligns with the definition of compound options as well. Each type of compound option does have two distinct expiration dates and strike prices - one for the initial option and one for the underlying secondary option.

Choice D is incorrect. Not all features are consistent with a compound option's definition.