Chapter 26

Accounting for Derivatives: A Primer

Ira G. Kawaller

Kawaller & Co

26.1 Overview

26.2 Definition of a Derivative

26.3 Exemptions

26.4 Embedded Derivative Instruments

26.5 Accounting Treatment

(a) Cash Flow Hedges

(i) Exposures That Qualify for Cash Flow Hedge Accounting

(ii) Eligible Risks

(iii) Prerequisite Requirements

(iv) Disallowed Situations

(v) Internal Derivatives Contracts

(b) Fair Value Hedges

(i) Examples

(ii) Eligible Risks

(iii) Prerequisite Requirements

(iv) Disallowed Situations

(c) Hedges of Net Investments in Foreign Operations

(d) Hedge Effectiveness

(e) Speculative Trades or Trades Not Qualifying for Hedge Accounting

26.6 Disclosures

(a) All Reporting Entities

(b) Hedging

(c) Fair Value Hedges

(d) Cash Flow Hedges

26.7 International Financial Reporting Standards and Derivatives

26.8 Sources and Suggested References

26.1 Overview

It would be easy for us to dismiss [derivatives] as [investment products] only sophisticated investors use minimizing any impact to our economy.…If we think back to the collapse of Enron, or even farther back to Long-Term Capital Management, we understand how the abuse of derivatives can have a negative impact not only on the parties to the contract, but also on the market and the economy.

—Rep. Richard Neal, D-Mass., chairman of the House Ways and Means Select Revenue Measures Subcommittee, at a March 5 (2008) hearing on tax treatment of derivatives

Originally issued as Financial Accounting Statement (FAS) No. 133, Accounting for Derivative Instruments and Hedging Activities, the rules for accounting for derivatives and hedging transactions are found under the Accounting Standard Codification (ASC) 815, Derivatives and Hedging. This chapter an overview of these rules. It is designed to highlight only the more critical features of the standard, and it may omit relevant guidance for specific situations.

The single inviolate accounting requirement for derivatives is that they must be marked to market and recorded as assets or liabilities on the balance sheet. Beyond that, the accounting treatment will depend on the intended use of the derivative and/or whether specific conditions have been satisfied.

For speculative purposes, derivative gains or losses must be marked to market, and gains or losses are recorded in the current period's income. When hedging exposures associated with the price of an asset, liability, or a firm commitment, accounting for the derivative is the same as it is for speculative uses. In addition, however, the underlying exposure must also be marked to market due to the risk being hedged; and these results must flow through current income as well. This treatment is called a fair value hedge.

A hedge of an upcoming, forecasted event would be a cash flow hedge. For cash flow hedges, derivative results must be evaluated, with a determination made as to how much of the result is effective and how much is ineffective. The ineffective component of the hedge results must be recorded in current income while the effective portion is initially posted to other comprehensive income (OCI) and later reclassified to income in the same time frame in which the forecasted cash flow affects earnings. Importantly, as of this writing, the Financial Accounting Standards Board (FASB) recognizes hedges as being ineffective for accounting purposes only when the hedge effects exceed the effects of the underlying forecasted cash flow, measured on a cumulative basis; however, this asymmetric provision is under consideration and is subject to change.

Finally, the last category qualifying for special accounting treatment is the hedge associated with the currency exposure of a net investment in a foreign operation. Again, the hedge must be marked to market. This time, the treatment requires effective hedge results to be consolidated with the translation adjustment in OCI. Any excess of hedge results relative to the risk being hedged would be recorded in earnings.

26.2 Definition of a Derivative

According to ASC 815-10-15, a qualifying derivative must satisfy three criteria:

26.3 Exemptions

Complicating the process for assessing whether any contractual arrangement qualifies as a derivative is the fact the FASB has scoped out a host of situations that might otherwise appear to satisfy the given definition (see Accounting Standards Codification (ASC) 815-10-15). For example:

• Regular-way securities trades, where delivery occurs within the time frame of normal market conventions.
• Normal purchases and normal sales where instruments will be delivered in amounts expected to be used within a reasonable period of time in the normal course of business and where there is a high probability that the contracts will result in physical deliver. Contracts that required periodic cash settlements (e.g., futures contracts) do not qualify for this exception.
• Certain types of insurance are exempt from treatment as a derivative if the payout compensates the insured for an identifiable insurable event other than a change in price.
• Financial guarantee contracts that reimburse for specific losses due to defaults of debtors.
• Off-exchange contracts where settlement amounts are based on (a) climactic, geological, or other physical variables; (b) prices of nonfinancial assets or liabilities on either party to the contract, where the underlying instrument is not readily convertible to cash; or (c) specific volumes of sales or revenues of one of the parties to the contract.
• Derivatives that serve as impediments to sales accounting.
• Contracts (a) indexed to a company's own stock and classified in stockholders' equity; (b) issued by the reporting entity relating to stock-based compensation; or (c) issued as a contingent consideration from a business combination.

26.4 Embedded Derivative Instruments

Embedded derivatives are components of contractual arrangements that, by themselves (i.e., on a stand-alone basis), would satisfy the criteria in the definition of a derivative. Embedded derivatives are often present in structured note contracts and other debt obligations, but they may also be found in such contracts such as leases, purchase agreements, insurance contracts, guarantees, and other tailored arrangements. Embedded derivatives reside in host contracts; and the combined instrument (i.e., the host and the embedded derivative) is referred to as the hybrid instrument. An example of an embedded derivative is a convertible bond. The host security is the debt instrument, and the embedded derivative is the option to convert the bond.

In general, embedded derivatives must be separated from the host contract for accounting purposes. Provided they meet the qualifying criteria for being a derivative under the FASB criteria, embedded derivatives must be accounted for as if they were free-standing derivatives, unless (1) the characteristics and risks of the embedded derivative are clearly and closely related to those of the host, or (2) the hybrid instrument is remeasured at fair value with changes reported in earnings.

According to ASC 815-15-25, if the embedded derivative incorporates a leverage factor or if an investor may not recover substantially all of the initial recorded investment, the embedded derivative would be required to be accounted for separately from the host.

ASC 815-10-15 states that interest-only and principal-only strips are specifically exempted from being treated as derivatives, provided that (1) the original securities from which these derivatives were constructed have no embedded derivatives that would otherwise be covered under FAS 133, and (2) the strips do not contain any features that were not initially a part of the original instrument.

ASC 815-15-10 also states that embedded foreign currency derivatives are exempt from treatment as a derivative if (1) the host is not a financial instrument and settlements are required in the functional currency of any substantial party to the contract, or (2) the settlements are denominated in the currency of the price that is routinely used for international commerce of the underlying good or service.

26.5 Accounting Treatment

The accounting treatment that applies to any given derivatives position may vary, depending on whether the derivative is used as a hedging instrument or not. Even assuming the derivative is intended as a hedge, one cannot simply elect to apply special hedge accounting. The exposure being hedged must qualify as a permissible hedged item, and the intended hedging relationship much be documented as such. If this documentation is not complete as of the trade date of the derivative contract, the hedge could not be applied, and the derivative would have to be marked to market through earnings. Critically, failure to have the documentation in place when the derivative is traded does not preclude drafting this documentation later, at which time hedge accounting could be instituted.

With the determination that the derivative is to be used as a hedge and with all the necessary prerequisites satisfied, the appropriate accounting treatments would depend on the nature of the hedge. Three different types of hedge treatments are cash flow hedges, fair value hedges, and hedges of net investments in foreign operations.

Derivatives that are not intended to serve as hedges—or derivatives that fail to qualify for hedge accounting treatment—must be accorded the regular accounting treatment, which is generally referred to as accounting for speculative derivative transactions.

• When seeking special hedge accounting, hedges must be documented at the inception of the hedge, with the objective and strategy stated, along with an explicit description of the methodology used to assess hedge effectiveness. This documentation must include the identification of the hedged item and the hedging instrument and the nature of the risk being hedged. This documentation must include (among other things) discussion relating to hedge effectiveness.
• A qualifying condition to apply hedge accounting is that derivatives' gains must be expected to be “highly effective at offsetting changes in fair values or cash flows of associated with the risks being hedged. The documentation further requires both a prospective assessment of hedge effectiveness and a retrospective assessment. The former justifies the expectation of high effectiveness before the fact; the latter validates that the hedge performance actually was sufficiently effective, after the fact. Satisfying both assessments is required before hedge accounting is permitted.

(a) Cash Flow Hedges

A hedge of an upcoming, forecasted event is a cash flow hedge. To qualify for cash flow hedge treatment, a key requirement is that exposure involves the risk of an uncertain (i.e., variable) cash flow. Derivative results must be evaluated, with a determination made as to how much of the result is effective and how much is ineffective. The ineffective component of the hedge results must be reported in current income, while the effective portion is initially posted to OCI and later reclassified to income in the same time frame in which the forecasted cash flow affects earnings.

For purposes of determining the amount that is appropriate to be posted to OCI, this assessment must be made on a cumulative basis. According to ASC 815-30-35, contributions to earnings are currently required only if the derivative results exceed the cash flow effects of the hedged items. This provision is currently under consideration and subject to change, whereby ineffective earnings amounts would be determined symmetrically, reflecting either excess hedge results or shortfalls.

Cash flow hedge accounting is not automatic. Specific criteria must be satisfied both at the inception of the hedge and on an ongoing basis. If, after initially qualifying for cash flow accounting, the criteria for hedge accounting stop being satisfied, hedge accounting is no longer appropriate. According to ASC 815-30-40, with the discontinuation of hedge accounting, any accumulated OCI would remain there, unless (except in extenuating circumstances) it is probable that the forecasted transaction will not occur by the end of the originally specified time period or within an additional two-month period of time thereafter.

ASC 815-30-40 indicates that reporting entities have complete discretion to undesignate cash flow hedge relationships at will and later redesignate them, assuming all hedge criteria are again (or still) satisfied. This provision is also under consideration and subject to change. While such flexibility affords management the opportunity to most fairly present the financial numbers in economic terms, such flexibility can also lead to accounting manipulation.

(i) Exposures That Qualify for Cash Flow Hedge Accounting

Examples of exposures that qualify for cash flow hedge accounting include:

• Interest rate exposures that relate to a variable or floating interest rates
• Planned purchases or sales of assets
• Planned issuances of debt or deposits
• Planned purchases or sales of foreign currencies
• Currency risk associated with prospective cash flows that are not denominated in the functional currency

(ii) Eligible Risks

The risk being hedge in a designated hedging relation must be explicitly stated in the hedge documentation. The following details explicit risk categories that are permitted to be afforded hedge accounting (ASC topic 815-20-25)

• Currency risk associated with (1) a forecasted transaction in a currency other than the functional currency, (2) an unrecognized firm commitment, or (3) a recognized foreign currency–denominated debt instrument.
• The entire price risk associated with purchases or sales of nonfinancial goods. That is, unless the purchase or sale specifically relates to buying or selling individual components, the full price of the good in question must be viewed as the hedged item.
• For financial instruments, hedgeable exposures include cash flow effects to:

(iii) Prerequisite Requirements

To qualify for cash flow accounting treatment, ASC 815-20-25 states that these prerequisites apply:

• Hedges must be documented at the inception of the hedge, with the objective and strategy stated, along with an explicit description of the methodology used to assess hedge effectiveness.
• Dates (or periods) for the expected forecasted events and the nature of the exposure involved (including quantitative measures of the size of the exposure) must be explicitly documented.
• The hedge must be expected to be “highly effective,” both at the inception of the hedge and on an ongoing basis. Effectiveness measures must relate the gains or losses of the derivative to changes in the cash flows associated with the hedged item.
• The forecasted transaction must be probable.
• The forecasted transaction must be made with a different counterparty than the reporting entity.

(iv) Disallowed Situations

According to ASC 815-20-25, cash flow accounting may not be applied under the following circumstances:

• In general, written options may not serve as hedging instruments. An exception to this prohibition (i.e., when a written option may qualify for cash flow accounting treatment) is when the hedged item is a long option.
• In general, basis swaps do not qualify for cash flow accounting treatment unless both of the variables of the basis swap are linked to two distinct variables associated with two distinct cash flow exposures.
• Cross-currency interest rate swaps do not qualify for cash flow hedge accounting treatment if the combined position results in exposure to a variable rate of interest in the functional currency. This hedge would qualify, however, as a fair value hedge.
• With held-to-maturity fixed income securities under Statement No. 115, Accounting for Certain Investments in Debt and Equity Securities, interest rate risk may not be designated as the risk exposure in a cash flow relationship.
• The forecasted transaction may not involve a business combination subject to Opinion No. 16, Business Combinations, and does not involve

• Prepayment risk may not be designated as the hedged item.
• The interest rate risk to be hedged in a cash flow hedge may not be identified as a benchmark interest rate, if a different variable interest rate is the specified exposure—for example, if the exposure is the risk of a higher prime rate, LIBOR may not be designated as the risk being hedged.

(v) Internal Derivatives Contracts

Except in the case when currency derivatives are used in cash flow hedges, derivatives between members of a consolidated group (i.e., internal derivatives) cannot qualify as hedging instruments in the consolidated statement, unless offsetting contracts have been arranged with unrelated third parties on a one-time basis (ASC topic 815-20-25).

For an internal currency derivative to qualify as a hedging instrument in a consolidated statement, it must be used as a cash flow hedge only for a foreign currency forecasted borrowing, a purchase or sale, or an unrecognized firm commitment, , subject to the following conditions:

• The nonhedging counterpart to the internal derivative must offset its net currency exposure with a third party within 3 days of the internal contract's hedge designation date.
• The third-party derivative must mature within 31 days of the internal derivative's maturity date.

(b) Fair Value Hedges

When hedging exposures associated with the price of an asset, liability, or a firm commitment, the total gain or loss on the derivative is recorded in earnings. In addition, the carrying value of the underlying exposure must be adjusted by an amount attributable to the risk being hedged; and these results flow through current income as well. This treatment is called a fair value hedge. Hedgers may elect to hedge all or a specific identified portion of any potential hedged item.

According to ASC 815-25-40, fair value hedge accounting is not automatic. Specific criteria must be satisfied both at the inception of the hedge and on an ongoing basis. If, after initially qualifying for fair value accounting, the criteria for hedge accounting stop being satisfied, hedge accounting is no longer appropriate. With the discontinuation of hedge accounting, gains or losses of the derivative will continue to be recorded in earnings but no further basis adjustments to the original hedged item would be made.

ASC 815-25-40 states that reporting entities have complete discretion to dedesignate fair value hedge relationships at will and later redesignate them, assuming all hedge criteria remain. As noted earlier, this provision is under reconsideration and subject to change.

(i) Examples

According to ASC 815-25-40, these exposures may qualify for fair value hedge accounting:

• Interest exposures associated with the opportunity cost of fixed rate debt
• Price exposures for fixed rate assets
• Price exposures for firm commitments associated with prospective purchases or sales
• Price exposures associated with the market value of inventory items
• Price exposures on available-for-sale securities.

(ii) Eligible Risks

These are examples of risks that can qualify for fair value hedge accounting (ASC 815-20-25):

• The risk of the change in the overall fair value
• The risk of changes in fair value due to changes in the benchmark interest rates (i.e., the risk-free rate of interest or the rate associated with LIBOR-based swaps), foreign exchange rates, creditworthiness, or the spread over the benchmark interest rate relevant to the hedged item's credit risk
• Currency risk associated with (1) an unrecognized firm commitment, (2) a recognized foreign currency–denominated debt instrument, or (3) an available-for-sale security.

(iii) Prerequisite Requirements

According to ASC 815-20-25, to qualify for fair value accounting treatment these prerequisites must be satisfied:

• Hedges must be documented at the inception of the hedge, with the objective and strategy stated, along with an explicit description of the methodology used to assess hedge effectiveness.
• The hedge must be expected to be “highly effective,” both at the inception of the hedge and on an ongoing basis. Effectiveness measures must relate the gains or losses of the derivative to those changes in the fair value of the hedged item that are due to the risk being hedged.
• If the hedged item is a portfolio of similar assets or liabilities, each component must share the risk exposure, and each item is expected to respond to the risk factor in comparable proportions.
• Portions of a portfolio may be hedged if they are:

• A change in the fair value of the hedged item must present an exposure to the earnings of the reporting entity.

Fair value hedge accounting is permitted when cross-currency interest rate swaps result in the entity being exposed to a variable rate of interest in the functional currency

(iv) Disallowed Situations

ASC 815-20-25 states that fair value accounting may not be applied in these situations:

• In general, written options may not serve as hedging instruments. An exception to this prohibition (i.e., when a written option may qualify for cash flow accounting treatment) is when the hedged item is a long option. Any combinations that include written options and involve the net receipt of premium—either at the inception or over the life of the hedge—are considered to be written option positions.
• Assets or liabilities that are remeasured with changes in value attributable to the hedged risk reported in earnings—for example, nonfinancial assets or liabilities that are denominated in a currency other than the functional currency—do not qualify for hedge accounting. The prohibition does not apply to foreign currency–denominated debt instruments that require remeasurement of the carrying value at spot exchange rates.
• Investments accounted for by the equity method do not qualify for hedge accounting.
• Equity investments in consolidated subsidiaries are not eligible for hedge accounting.
• Firm commitments to enter into business combinations or to acquire or dispose of a subsidiary, a minority interest, or an equity method investee are not eligible for hedge accounting.
• A reporting entity's own equity is not eligible for hedge accounting.
• For held-to-maturity debt securities, the risk of a change in fair value due to interest rate changes is not eligible for hedge accounting. Fair value hedge accounting may be applied to a prepayment option that is embedded in a held-to-maturity security, however, if the entire fair value of the option is designated as the exposure.
• Prepayment risk may not be designated as the risk being hedged for a financial asset.
• Except for currency derivatives, derivatives between members of a consolidated group cannot be considered to be hedging instruments in the consolidated statement, unless offsetting contracts have been arranged with unrelated third parties on a one-time basis.

(c) Hedges of Net Investments in Foreign Operations

Special hedge accounting is appropriate for hedges of the currency exposure associated with net investments in foreign operations, which give rise to translation gains or losses that are recorded in the currency translation account (CTA) in shareholders' equity. ASC 815-20-25-66 states that derivatives and nonderivatives (i.e., assets or liabilities denominated in the same currency as that of the net investment) may be designated as hedges of these exposures. According to ASC 815-20-35-1, effective results of such hedges are recognized in the same manner as a translation adjustment. Ineffective portions of hedge results are recognized in earnings.

Hedge accounting for net investments in foreign operations is not automatic. Specific criteria must be satisfied both at the inception of the hedge and on an ongoing basis. If, after initially qualifying, the criteria for hedge accounting stop being satisfied, hedge accounting is no longer appropriate. With the discontinuation of hedge accounting, gains or losses of the derivative will be recorded in earnings.

Reporting entities have complete discretion to hedge relationships at will and later redesignate them, assuming all hedge criteria remain satisfied.

(d) Hedge Effectiveness

As noted above, to qualify for special hedge accounting, ASC 815-20-25-79 states that hedge effectiveness must be assessed prospectively (i.e., before the fact) and retrospectively (after the fact, but no less frequently than quarterly). The methods used to for these effectiveness assessments must be defined with the hedge documentation; and these methods must be applied as prescribed. If the entity decides to improve on these methods, the original hedge must be dedesignated and a new hedge relationship needs to be stipulated. According to ASC 815-20-25-81, if the same method is not applied to similar hedges, a justification for using differing methods is required.

Entities may elect to exclude specific components of hedge results from the hedge effectiveness assessment. ASC 815-20-25-82 indicates that allowable excluded items are (1) differences between spot and forward (or futures prices), if the derivative is or contains a forward or futures contract; or (2) the time value or the volatility value of options, if the derivative is or contains an option contract.

As a rule, whenever the underlying exposure relates to a price, interest rate, or currency exchange rate that is not precisely identical to the underlying of the associated hedging derivative, some degree of hedge ineffectiveness must be expected. According to ASC 815-20-25-84, however, when entities are able to clearly identify and enter into a hypothetical derivative—that is, a derivative that perfectly offsets the changes in fair values or cash flows of the designated hedged item—they can and should expect the hedge to perform perfectly, generating no earnings impacts attributable to hedge ineffectiveness.

The FASB has not sanctioned any particular methodology for assessing hedge effectiveness, and devising such tests is often nontrivial. Hedging entities are encouraged to discuss their intended approaches with their external auditors prior to initiating any hedging transactions.

(e) Speculative Trades or Trades Not Qualifying for Hedge Accounting

The accounting treatment is the same for derivatives intended for speculative purposes or for situations in which the prerequisite hedge criteria are not satisfied. Derivatives are recorded on the balance sheet at fair market value, and gains and losses are realized in earnings. The objective for using the derivative contract(s) must still be disclosed.

26.6 Disclosures

(a) All Reporting Entities

ASC 815-50-10-1 states that all reporting entities that use derivative instruments must disclose:

• Objectives for using each derivative, whether for hedging or for speculation
• The context needed to understand objectives—that is, how the derivative affects the entity's financial position, financial performance, and cash flows
• The location and fair value amounts of derivative reported in the statement of financial performance or the statement of financial position

Qualitative disclosures are encouraged.

(b) Hedging

ASC 815-50-10-4 states that if derivatives are used in hedging relationships, the next issues must be disclosed:

• Risk management policies must be specified, identifying exposures to be hedged and hedging strategies for managing the associated risks.
• The type of hedging relationship (i.e., fair value, cash flow, net investment in foreign operation) must be identified, if applicable.
• The hedged item must be explicitly identified.
• Ineffective hedge results must be disclosed.
• Any component of the derivatives' results that is excluded from the hedge effectiveness assessment must be disclosed.
• The location and amount of the gains and losses on any related hedged items reported in the statement of financial performance or the statement of financial position must be indicated.

(c) Fair Value Hedges

According to 815-25-50, there are specific disclosure requirements for fair value hedges, such as disclosing the place on the income statement where derivative gains or losses are reported. When a firm commitment no longer qualifies as a hedged item, the net gain or loss recognized in earnings must be disclosed.

(d) Cash Flow Hedges

According to ASC 815-30-50, there are specific requirements for cash flow hedges:

• A description of the conditions that will result in the reclassification of accumulated OCI into earnings and a schedule of the estimated reclassification expected in the coming 12 months must be disclosed.
• The maximum length of time over which hedging is anticipated (except for variable interest rate exposures) must be disclosed.
• Entities must disclose the amount reclassified into earnings as a result of discontinued cash flow hedges because the forecasted transaction is no longer probable.

There are specific requirements for hedges of net investments in foreign operations. Entities must disclose the amount of the derivatives' results that is included in the cumulative translation adjustment during the reporting period.

26.7 International Financial Reporting Standards and Derivatives

As is true with most accounting areas of complexity, the march toward international standards is dotted with potholes and issues. While some features of International Accounting Standard (IAS) No. 39, Financial Instruments: Recognition and Measurement and U.S. generally accepted accounting principles (GAAP) are shared, some differences will need to be resolved as countries move toward congruence. Generally the IAS tracks GAAP in the criteria used to qualify a hedge, but in a cash flow hedge, U.S. GAAP treats unrealized gains and losses as part of equity (OCI) until realized. Under IAS No. 39, that change in value is recorded as an adjustment to the value of the hedged item. As another example, GAAP does not permit the hedging of a portion of the cash flows, but International Financial Reporting Standards (IFRS) do. These and other differences mean that more thinking on the best accounting in this critically important area² is forthcoming.

26.8 Sources and Suggested References

American Institute of Certified Public Accountants. Auditing Derivative Instruments, Hedging Activities, and Investments in Securities. AICPA Audit Guide. New York, AICPA April 2011.

Banks, E. Exchange Traded Derivatives. Hoboken, NJ: John Wiley & Sons, 2002.

Financial Accounting Standards Board. Statement of Financial Accounting Standards No. 133, Accounting for Derivative Instruments and Hedging Activities. Stamford, CT: Author, 1998.

_____. Statement of Financial Accounting Standards No. 157, Fair Value Measurement. Norwalk, CT: Author, 2006.

_____. Statement of Financial Accounting Standards No. 159, The Fair Value Option for Assets and Liabilities. Norwalk, CT: Author, 2007.

_____. Accounting Standards Update (ASU No. 2011-04), Fair Value Measurement (Topic 820)—Amendments to Achieve Common Fair Value Measurement and Disclosure Requirements in U.S. GAAP and IFRS. Norwalk, CT: Author, 2011

_____. Accounting Standards Update No. 2010-11, Derivatives and Hedging (Topic 815) Scope Exception Related to Embedded Credit Derivatives. Norwalk, CT: Author, 2011.

Flavell, R. Swaps and Other Derivatives. Hoboken, NJ: John Wiley & Sons, 2010.

Heye, P., “How to Manage Fluctuations in Foreign Currency Rates,” Journal of Accountancy (April 2011).

Kawaller, I. www.kawaller.com/articles.shtml (link to the extensive published literature and articles by the author of this chapter)

Kolb, R., and J. Overdahl (eds.). Financial Derivatives: Pricing and Risk Management. Hoboken, NJ: John Wiley & Sons, 2009.

¹ While the underlying is the variable in a derivative, the notional amount is the fixed amount or quantity that determines the size of the change caused by the movement of the underlying. Examples include the stated principal amount in an interest rate swap, the stated number of bushels in a wheat futures contract, and the contracted amount of euros in a foreign currency forward.

² It is reported that at the end of 2009, there were around $450 trillion in derivative contracts in play. See P. Eavis, “Bill on Derivatives Overhaul Is Long Overdue,” Wall Street Journal, April 4, 2010.