How can the necessary Notional Principal (NP) on an interest rate swap be calculated to close the duration gap to zero?

To determine how the necessary Notional Principal (NP) on an interest rate swap can adjust the balance of the duration gap, it's crucial to understand the concepts of Basis Point Value (BPV) and how they relate to the asset and liability side of a balance sheet.

The condition given in choice A, which states that Asset BPV plus the product of Notional Principal and Swap BPV divided by 100 equals Liability BPV, represents a fundamental relationship in managing the interest rate risk exposure through swaps.

When adjusting for the duration gap to achieve a zero duration gap, the goal is to ensure that the BPVs of the assets and liabilities are equal. This balancing act involves adding or subtracting BPV contributions from the swap based on the notional amount. Since BPV is sensitive to the notional amount of the swap and reflects the change in the value of a portfolio for a one basis point change in interest rates, the equation recognizes that the addition of NP multiplied by the Swap BPV will effectively increase the total BPV of assets to match that of liabilities.

Therefore, rearranging the equation highlights how you can compute NP, which is essential in mitigating the duration gap risk. The equality holds true in ensuring that the present value interest exposure