The correct answer is A.

During periods of falling interest rates, homeowners are more likely to refinance their mortgage loans. Refinancing allows homeowners to replace their existing mortgage with a new one that has a lower interest rate. This process accelerates prepayments because homeowners are paying off their old mortgage faster than originally planned. Prepayments are the early return of principal on a mortgage security. When prepayments accelerate, the average life of the mortgage-backed security (MBS) reduces. The average life of an MBS is the weighted-average time to the return of a dollar of principal, measured in years. When homeowners prepay their mortgages, the principal is returned sooner, reducing the average life of the MBS.

Choice B is incorrect. Falling interest rates typically encourage borrowers to refinance their mortgage loans, which accelerates prepayments. This in turn reduces the average life of the MBS, not increase it as this option suggests.

Choice C is incorrect. While it's true that falling interest rates accelerate prepayments due to increased refinancing activity, this actually reduces the average life of the MBS rather than increasing it. The faster prepayment speed means that investors receive their principal back sooner than expected, thus shortening the average life of the security.

Choice D is incorrect. This choice incorrectly suggests that falling interest rates decelerate prepayments and decrease the average life of MBS. In reality, lower interest rates lead to an acceleration in prepayments due to increased refinancing activity by borrowers and consequently reduce (not decrease) the average life of MBS.