Use of Derivatives to Manage Interest Rate Risk. We use or have used various derivative financial instruments to manage our exposure to fluctuations in interest rates, including interest rate swaps, interest rate options, TBA forwards, bond forwards, treasury forwards, swaptions and futures. We use interest rate swaps, treasury forwards and futures contracts to hedge against changes in the value of the GMWB MRB. We use interest rate swaps and have used TBA forwards primarily to more closely match the interest rate characteristics of assets and liabilities. They can be used to change the sensitivity to the interest rate of specific assets and liabilities as well as an entire portfolio. We use bond forwards to fix the purchase price of a bond at a specified date in the future. We use interest rate options to manage prepayment risks in our assets and minimum guaranteed interest rates and lapse risks in our liabilities. We have purchased swaptions to hedge interest rate exposure for certain assets and liabilities.
Foreign Currency Risk
Foreign currency risk is the risk we will incur economic losses due to adverse fluctuations in foreign currency exchange rates. This risk arises from foreign currency-denominated funding agreements issued to nonqualified institutional investors in the international market, foreign currency-denominated fixed maturity and equity securities, and our international operations, including expected cash flows and potential acquisition and divestiture activity.
We estimate as of September 30, 2023, a 10% immediate unfavorable change in each of the foreign currency exchange rates to which we are exposed would result in no material change to the net fair value of our foreign currency-denominated instruments identified above because we effectively hedge foreign currency-denominated instruments to minimize exchange rate impacts, which is consistent with our estimate as of December 31, 2022. However, fluctuations in foreign currency exchange rates do affect the translation of segment pre-tax operating earnings and equity of our international operations into our consolidated financial statements.
For our Principal International operations, we estimate that a 10% immediate unfavorable change in each of the foreign currency exchange rates to which we were exposed would have resulted in a $294.5 million, or 10.0%, reduction in the total equity excluding noncontrolling interests of our international operations as of September 30, 2023, as compared to an estimated $258.5 million, or 10.0%, reduction as of December 31, 2022. We estimate a 10% unfavorable change in the average foreign currency exchange rates to which we were exposed through our international operations would have resulted in an $8.8 million, or 12.0%, reduction in segment pre-tax operating earnings of our international operations for the three months ended September 30, 2023, as compared to an estimated $8.3 million, or 13.0%, reduction for the three months ended September 30, 2022. In addition, we estimate that a 10% unfavorable change in the average foreign currency exchange rates to which we were exposed through our international operations would have resulted in a $26.4 million, or 12.0%, reduction in segment pre-tax operating earnings of our international operations for the nine months ended September 30, 2023, as compared to an estimated $27.3 million, or 12.0%, reduction for the nine months ended September 30, 2022.
The selection of a 10% immediate unfavorable change in all currency exchange rates should not be construed as a prediction by us of future market events, but rather as an illustration of the potential impact of such an event. These exposures will change as a result of a change in the size and mix of our foreign operations.
Use of Derivatives to Manage Foreign Currency Risk. The foreign currency risk on funding agreements and fixed maturities in our U.S. operations is mitigated by using currency swaps that swap the foreign currency interest and principal payments to our functional currency. We did not have currency swap agreements associated with foreign-denominated liabilities as of September 30, 2023 and December 31, 2022. The notional amount of our currency swap agreements associated with foreign-denominated fixed maturities was $1,540.0 million and $1,389.8 million as of September 30, 2023 and December 31, 2022, respectively.
With regard to our international operations, in order to enhance the diversification of our investment portfolios we may invest in bonds denominated in a currency that is different than the currency of our liabilities. We use foreign exchange derivatives to economically hedge the currency mismatch. Our Principal International operations had currency swaps with a notional amount of $217.3 million and $244.9 million as of September 30, 2023 and December 31, 2022, respectively. Our Principal International operations also utilized currency forwards with a notional amount of $726.8 million and $672.5 million as of September 30, 2023 and December 31, 2022, respectively.
We use currency forwards to hedge currency risk associated with expected cash flows in our foreign operations. We held currency forwards with a notional of $204.7 million and $388.5 million as of September 30, 2023 and December 31, 2022, respectively.
