First Principles Thinking: core idea
A is correct. The CFA Curriculum defines modified duration as the slope, or first derivative, of a bond’s price with respect to its yield-to-maturity. The rule is that it measures how sensitive price is to a change in yield. The intuition is that duration summarizes interest rate risk in one number. Applying that rule identifies yield-to-maturity as the variable that modified duration measures price sensitivity against.
Why top distractor is wrong :. Coupon frequency matters in bond pricing, but modified duration is not defined as sensitivity to coupon frequency only.
Why remaining distractor is wrong. Face value affects price level, but modified duration is not defined as sensitivity to face value changes.