Explanation

The key difference between the Black model and the standard market model is:

Black model: Assumes the underlying is a forward price Standard market model: Assumes the underlying is a futures price

This distinction is important because:

• Forward prices and futures prices differ due to the daily settlement feature of futures
• The Black model is more commonly used for interest rate options where the underlying is typically a forward rate
• The standard market model is more appropriate for options on futures contracts

Therefore, option A is correct: the standard market model assumes the underlying is a futures price.