Fair value is defined as the price at which an orderly transaction to sell an asset or to transfer a liability would take place between market participants at the measurement date under current market conditions (that is, an exit price at the measurement date from the perspective of a market participant that holds the asset or owes the liability).

Fair Value Hierarchy

The following hierarchy for inputs used in measuring fair value should maximize the use of observable inputs and minimize the use of unobservable inputs by requiring that the most observable inputs be used when available:

Level 1 — Quoted prices in active markets for identical assets or liabilities that are accessible at the measurement dates.

Level 2 — Significant other observable inputs that are used by market participants in pricing the asset or liability based on market data obtained from independent sources.

Level 3 — Significant unobservable inputs we believe market participants would use in pricing the asset or liability based on the best information available.

Derivatives

We are exposed to market risk attributable to changes in interest rates, foreign currency exchange rates and fuel prices. We attempt to minimize these risks through a combination of our normal operating and financing activities and through the use of derivatives. We assess whether derivatives used in hedging transactions are “highly effective” in offsetting changes in the cash flow of our hedged forecasted transactions. We use regression analysis for this hedge relationship and high effectiveness is achieved when a statistically valid relationship reflects a high degree of offset and correlation between the fair values of the derivative and the hedged forecasted transaction. There are no amounts excluded from the assessment of hedge effectiveness and there are no credit-risk-related contingent features in our derivative agreements. We monitor concentrations of credit risk associated with financial and other institutions with which we conduct significant business. Credit risk, including but not limited to counterparty non-performance under derivatives, is not considered significant, as we primarily conduct business with large, well-established financial institutions with which we have established relationships, and which have credit risks acceptable to us, or the credit risk is spread out among many creditors. We do not anticipate non-performance by any of our significant counterparties.

As of September 30, 2018, we had fuel swaps, which are used to mitigate the financial impact of volatility of fuel prices pertaining to approximately 0.9 million metric tons of our projected fuel purchases, maturing through December 31, 2020.

As of September 30, 2018, we had foreign currency forward contracts, matured foreign currency options and matured foreign currency collars which are used to mitigate the financial impact of volatility in foreign currency exchange rates related to our ship construction contracts denominated in euros. The notional amount of our foreign currency forward contracts was €2.0 billion, or $2.3 billion based on the euro/U.S. dollar exchange rate as of September 30, 2018.

As of September 30, 2018, we had interest rate swap agreements which are used to hedge our exposure to interest rate movements and manage our interest expense. The notional amount of our outstanding debt associated with the interest rate swap agreements was $1.0 billion as of September 30, 2018.

The derivatives measured at fair value and the respective location in the consolidated balance sheets include the following (in thousands):

The fair values of swap and forward contracts are determined based on inputs that are readily available in public markets or can be derived from information available in publicly quoted markets. The Company determines the value of options and collars utilizing an option pricing model based on inputs that are either readily available in public markets or can be derived from information available in publicly quoted markets. The option pricing model used by the Company is an industry standard model for valuing options and is used by the broker/dealer community. The inputs to this option pricing model are the option strike price, underlying price, risk-free rate of interest, time to expiration, and volatility. The fair value of option contracts considers both the intrinsic value and any remaining time value associated with those derivatives that have not yet settled. The Company also considers counterparty credit risk and its own credit risk in its determination of all estimated fair values.

Our derivatives and financial instruments were categorized as Level 2 in the fair value hierarchy, and we had no derivatives or financial instruments categorized as Level 1 or Level 3. Our derivative contracts include rights of offset with our counterparties. We have elected to net certain assets and liabilities within counterparties when the rights of offset exist. We are not required to post cash collateral related to our derivative instruments.

The gross and net amounts recognized within assets and liabilities include the following (in thousands):

The effects of cash flow hedge accounting on accumulated other comprehensive income (loss) include the following (in thousands):

The effects of cash flow hedge accounting on the consolidated statements of operations include the following (in thousands):

The effects of cash flow hedge accounting on accumulated other comprehensive income (loss) include the following (in thousands):

The effects of cash flow hedge accounting on the consolidated statements of operations include the following (in thousands):

Long-Term Debt

As of September 30, 2018 and December 31, 2017, the fair value of our long-term debt, including the current portion, was $6,693.9 million and $6,448.6 million, respectively, which was $13.9 million and $23.5 million higher, respectively, than the carrying values. The difference between the fair value and carrying value of our long-term debt is due to our fixed and variable rate debt obligations carrying interest rates that are above or below market rates at the measurement dates. The fair value of our long-term debt was calculated based on estimated rates for the same or similar instruments with similar terms and remaining maturities resulting in Level 2 inputs in the fair value hierarchy. Market risk associated with our long-term variable rate debt is the potential increase in interest expense from an increase in interest rates. The calculation of the fair value of our long-term debt is considered a Level 2 input.

Other

The carrying amounts reported in the consolidated balance sheets of all other financial assets and liabilities approximate fair value.