December 31, 2020, the payments not hedged aggregated €5.0 billion, or $6.1 billion, based on the euro/U.S. dollar exchange rate as of December 31, 2020. The change from December 31, 2020 to September 30, 2021 was due to the addition of foreign currency hedges. We estimate that a 10% change in the euro as of September 30, 2021 would result in a $0.6 billion change in the U.S. dollar value of the foreign currency denominated remaining payments.
Fuel Price Risk
Our exposure to market risk for changes in fuel prices relates to the forecasted purchases of fuel on our ships. Fuel expense, as a percentage of our total cruise operating expense, was 18.0% and 25.4% for the three months ended September 30, 2021 and 2020, respectively, and 19.8% and 15.0% for the nine months ended September 30, 2021 and 2020, respectively. We use fuel derivative agreements to mitigate the financial impact of fluctuations in fuel prices and as of September 30, 2021, excluding fuel swaps for transactions that are no longer probable of occurrence, we had hedged approximately 47%, 35% and 14% of our remaining 2021, 2022 and 2023 projected metric tons of fuel purchases, respectively. As of December 31, 2020, we had hedged approximately 59%, 37% and 15% of our 2021, 2022 and 2023 projected metric tons of fuel purchases, respectively. The percentage of fuel purchases hedged changed between December 31, 2020 and September 30, 2021 primarily due to changes in forecasted purchases and the termination of certain fuel swaps.
We estimate that a 10% increase in our weighted-average fuel price would increase our anticipated 2021 fuel expense by $10.9 million. This increase would be offset by an increase in the fair value of all our fuel swap agreements of $4.8 million. Fair value of our derivative contracts is derived using valuation models that utilize the income valuation approach. These valuation models take into account the contract terms such as maturity, as well as other inputs such as fuel types, fuel curves, creditworthiness of the counterparty and the Company, as well as other data points.
Item 4. Controls and Procedures
Evaluation of Disclosure Controls and Procedures
Our management has evaluated, with the participation of our Chief Executive Officer and Chief Financial Officer, the effectiveness of our disclosure controls and procedures, as such term is defined in Rule 13a-15(e) under the Securities Exchange Act of 1934, as amended, as of September 30, 2021. There are inherent limitations in the effectiveness of any system of disclosure controls and procedures, including the possibility of human error and the circumvention or overriding of the controls and procedures. Accordingly, even effective disclosure controls and procedures can only provide reasonable assurance of achieving their control objectives. Based upon management’s evaluation, our Chief Executive Officer and Chief Financial Officer concluded that our disclosure controls and procedures were effective as of September 30, 2021 to provide reasonable assurance that the information required to be disclosed by us in the reports we file or submit under the Securities Exchange Act of 1934, as amended, is recorded, processed, summarized and reported within the time periods specified in the rules and forms of the SEC, and that it is accumulated and communicated to our management, including our Chief Executive Officer and Chief Financial Officer, as appropriate, to allow timely decisions regarding required disclosure.
Changes in Internal Control Over Financial Reporting
There have been no changes in our internal control over financial reporting during the quarter ended September 30, 2021 that have materially affected, or are reasonably likely to materially affect, our internal control over financial reporting.
Limitations on the Effectiveness of Controls
It should be noted that any system of controls, however well designed and operated, can provide only reasonable, and not absolute, assurance that the objectives of the system will be met. In addition, the design of any control system is based in part upon certain assumptions about the likelihood of future events. Because of these and other inherent limitations of control systems, there is only the reasonable assurance that our controls will succeed in achieving their goals under all potential future conditions.