### Derivative Instruments

**Introduction**

A security or contract whose value is dependent on or derived from the value of some underlying asset.

The main classes of derivative instruments are: forwards, futures, options (and their securitized equivalents, warrants) and swaps.

There are derivative contracts on currencies, commodities, equities, interest rates, credit or default events, indices and baskets in all these asset classes and combinations of all of them.

Derivatives can be exchange-traded or traded over-the-counter (OTC).

The latter are contracts between counterparties and are telephone and screen traded by banks outside the regulated exchanges.

The definitions on this page cover the general terms used in the derivatives markets to describe the instruments, positions, markets, contracts and risks found in them.

Some are used in the cash markets, some are used only in the derivatives markets.

Some have different meanings in derivatives markets than in the underlying cash markets.

The basic terms in the options market are covered later, and the more complex concepts from mathematics and statistics that are integral to the modelling of option prices are covered,

along with many of the best known pricing models.

**Accreting**

The notional principal amount of accreting instruments increases over their life according to a pre-set schedule or pre-defined index. Accreting instruments are useful for hedging liabilities expected to grow predictably, for example to hedge the step-by-step drawdown of a syndicated loan agreement. Accretion has been applied to caps, collars, floors and swaptions. See amortizing.

**Accrual**

The accumulation of interest or other payoffs between payment or reset dates.

**Aggregation**

The netting of positive and negative values of swaps affected by early termination allowed by some swap master agreements.

**Amortizing**

The notional principal amount of amortizing instruments decreases over their life according to a pre-set schedule or pre-defined index. Instruments that have been structured in this way include caps, collars, floors, swaps and swaptions. See accreting.

**Arbitrage**

Instruments that have identical characteristics and so are perfect substitutes should trade at the same price. If they do not, a risk-free profit can be generated by simultaneously selling the higher-priced asset and buying the lower-priced asset. True arbitrage is the identification and exploitation of such price anomalies. More generally the term arbitrage is used to mean profiting from differences in price between similar securities or from trades which are undertaken when prices have moved from some historical or theoretical path or relationship in the expectation of a move back to the statistical norm. This is also known as statistical arbitrage.

**Assignment**

Notice to an option writer that an option has been exercised. In the swap market, assignment is the transfer of a swap obligation to another counterparty.

**Back contract**

The longest maturity futures contract currently trading.

**Backwardation**

A commodity market is in backwardation when commodity futures prices are lower than spot prices to produce a negatively sloped forward curve. See contango.

**Barstrier**

Many derivatives, combinations of derivatives and structured notes have a payout determined or altered by the underlying trading at or through a particular level. The barrier, or trigger, is the price or rate at which these instruments are activated (knocked-in) or deactivated (knocked-out), or more generally, change their character in some pre-determined way.

**Basis**

(i) In futures markets, the price of the futures contract minus the spot price.

That is, the difference between the forward price/yield and spot price/yield of futures (and also options).

Basis is divided into carry basis and value or excess basis.

Carry basis is the theoretical price of the future, minus the spot price of the underlying asset, and is equal to the net cost of carry.

Value/excess basis is the difference between the theoretical price of the future and its market price.

(ii) More generally, the relationship between prices/yields in related markets.

(iii) The basis upon which interest rates are calculated for bond and money market instruments.

**Basis risk**

The risk that prices in the underlying cash market are not exactly correlated with prices in the futures market. Consequently basis risk is used more generally for the risk that hedges composed of offsetting positions in the cash and derivatives markets become unbalanced.

**Basis trading**

Trading the spread between the futures (or more generally derivatives) markets and the underlying cash market. See cash-and-carry arbitrage.

**Basket**

A selection of stocks, indices, commodities, currencies or interest rates which can either be traded as a unit themselves or which can be used as the underlying for a derivative product.

**Beta**

A measure of the sensitivity of an asset's return to the market. The returns on a security with a beta of one will move in line with the market; if beta is greater than one the security will exaggerate market returns; if it is less than one it will under-reflect market moves; and if beta is negative, security and market returns move in opposite directions. Beta is a measure of the systematic risk of a security relative to the market. Betas are additive, hence the beta of a portfolio is the weighted average of all the individual betas in a portfolio. The capital asset pricing model states that unique or unsystematic risk can be diversified away so that only systematic risk commands a risk premium. See Capital Asset Pricing Model.

**Binary**

Any derivative or derivative-linked instrument whose fixed payout is either made ('on') or not made ('off') depending on the level of the underlying. Also known as digital.

**Bootstrapping**

A general term for techniques used to decompose the prices of instrument in the market to the prices of instruments that are simpler, more fundamental or analytically more tractable.
It is most commonly used to describe the process of mapping a yield curve defined through a series of market instruments into a series of zero-coupon bonds but also applies, for instance, to the mapping of a term volatility surface indexed by strike and time to maturity to a local volatility surface indexed by spot and elapsed time. See implied forward rate, spot rate.

**Breakeven**

The price or time at which a derivative strategy has no gain or loss relative to another strategy, usually a cash position or a "do-nothing strategy". For example, the breakeven price of purchasing a call option is the strike price plus the option premium paid. The breakeven time of purchasing a knockout option is the time at which, if the option knocks out, the strategy of buying a knockout option and then a vanilla option for the remaining time is the same price as having bought a vanilla option to the maturity date in the first place.

**Callable**

Terminable early. Callable bonds can be redeemed at their pre-set dates and prices by the issuer. Callable swaps allow the fixed-rate payer to terminate the swap. Where the fixed-rate receiver has the right to terminate, the swap is known as puttable.

**Capital Asset Pricing Model (CAPM)**

A model describing the relationship between expected risk and expected return for financial assets. At its simplest, it takes the form of a linear relationship: Rj = rf + ßj (Rm - rf) where Rj is the expected return of a security ßj is the beta of the security Rm is the expected return of "the market", e.g. the stock market rf is the return on riskless assets

**Capped**

The payout of options, warrants or swaps is capped if it is limited to a maximum specified amount. The opposite of floored.

**Carry**

The benefit or cost of maintaining a position in the cash market due to interest rate differentials. For example, in a positive yield curve environment carry is positive if one receives the long (swap) rate and pays the short rate (Libor). In the FX markets, carry is positive if the interest rate of the borrowing (short) currency is less than the interest rate of the lending (long) currency.

**Cash-and-carry arbitrage**

A basis trade involving a long cash position exactly offset by a short futures position. The holder of the position believes that the futures contract is expensive. He shorts the future, borrows at money market rates to finance a long position in the underlying and either delivers the asset into the futures contract or waits for a narrowing of the basis and closes out the positions, in which case he effectively collects the yield on a synthetic money market instrument. Also called buying the basis. This arbitrage and its opposite, reverse cash-and-carry, ensure that cash and derivatives markets do not diverge too far. The currency market version is called covered interest arbitrage - the arbitrage that keeps the interest rate differential between two currencies equal to the difference in the spot and forward exchange rates.

**Cash settlement**

The closing of a derivatives position by marking it to market and settling outstanding obligations in cash instead of by physical delivery of the underlying asset. Most financial derivatives and almost all over-the-counter derivatives are settled in this way, except for OTC foreign-exchange options, which tend to be physically settled.

**Cheapest to deliver**

In some futures contracts the seller has a choice of which of a variety of underlying securities to deliver. The security which it is most advantageous for the seller to deliver is called the cheapest to deliver.

**Constant maturity swap (CMS)**

For each maturity for which it is available the CMS rate is an index consisting of swap rates adjusted to that constant maturity.

**Constant maturity treasury (CMT)**

CMT rates are indices consisting of the semi-annual yield of outstanding US Treasuries adjusted to a constant x-year maturity. So the 10-year CMT would be adjusted to a constant 10-year maturity. CMT rates are calculated daily by the Federal Reserve and published weekly.

**Contango**

A commodity market is in contango when futures prices are above spot prices. The opposite of backwardation.

**Contingency**

Dependence of strike price, payout or existence of a derivative product upon one or more uncertain variable. See also contingent swap.

**Convertibility risk**

The risk that a given currency cannot be freely exchanged/delivered for another freely exchangeable 'hard' currency. See sovereign risk guarantee.

**Convexity**

In a fixed-income instrument convexity is a measure of the way duration changes as interest rates change.

An instrument is said to have positive convexity if its value increases by more than duration predicts when interest rates drop and decreases by less than duration predicts when interest rates rise.

An instrument for which the opposite is true is said to have negative convexity.

For options convexity is a measure of the way delta (or, more generally, any of the first-order derivatives or greeks) changes as the underlying changes.

In this context (that is, with respect to delta) it is more commonly known as gamma.

**Country risk**

The political or legal risks incurred by a transaction in a particular country, particularly an emerging market.

**Cover**

A long or {shot} position in an instrument that offsets partially or wholly a short {long} position in another. So a covered call is the sale of call options while long the underlying instrument. Also known as a buy-write. The covered call creates a synthetic short put position (see put-call parity) and the writer of the option gives up any upside potential beyond the strike of the calls in exchange for the premium income. If he believes that the price of the underlying will exceed the strike, then this is a form of forward sale. The covered put is the sale of put options while short the underlying. Also known as targeted put selling because the writer is effectively targeting a price at which he will buy the underlying while increasing its yield by taking in option premium. A covered warrant is covered either by other warrants or by holdings of the underlying which entitles the holder to buy existing securities in a company at a preset price for a given period. Originally a feature of the Japanese cum-warrant bond market where warrants were stripped from bonds and then re-packaged, covered warrants have become popular in Germany and Switzerland (where they are sometimes known as stillhalter warrants.)

**Credit event**

An occurrence that leaves an obligor unable to fulfil its financial obligations. Particularly in credit derivatives transactions these events are carefully specified and the International Swap Dealers' Association has its own definitions for events that may constitute a credit event. These are: failure to pay, insolvency, cross-default, restructuring, repudiation, merger and downgrade.

**Credit risk**

The risk that the obligor or counterparty in a financial transaction defaults on their obligations under the terms of the transaction. The holder of a bond is exposed to the risk that the issuer undergoes a credit event and defaults on a coupon or principal payment. The counterparty to a swap is exposed to the risk that the other counterparty does not make payments due under the swap agreement.

**Currency protected**

Used for instruments which give the buyer exposure to a foreign index or asset without the exposure to the foreign currency that would normally follow. Derivatives that incorporate this feature are also variously described as currency translated, quantized/quantoed or differential. See currency protected option, currency protected FRA, currency protected swap, differential interest rate fix.

**Curve lock**

Any instrument or combination of instruments that locks in the spread between two different points on a yield curve.

**Deleveraged**

Used for derivatives or notes with embedded derivatives whose payoff is linked to a fraction of some index or variable, just as leveraged is used for instruments whose payoff is linked to a multiple of an index, spread or variable.

**Digital**

The same as binary.

**Duration**

Modified duration is the percentage change in the price of a fixed-income instrument per basis point change in yield. For a 1% change in yield, an instrument with a modified duration of 1.5 will change 1.5% in price in the opposite direction. Macaulay duration is the present value weighted-average term to maturity of a fixed-income instrument expressed in years. It is calculated as the average life of the present values of all future cashflows of an instrument with the time delay until receipt of each cashflow weighted by the contribution of that cashflow to the total present value of the instrument. Both are measures of price sensitivity to interest rate changes. The longer its duration, the more sensitive an instrument is to interest rates. Instruments whose price rises as rates rise are said to exhibit negative duration.

**Duration leverage**

Concentrating the risk of a longer-dated instrument (e.g. 10 years) in a shorter-dated one (e.g. three years). The principal amount of the three-year notes loses or gains value according to the mark-to-market value of the longer-dated one. See duration enhanced notes.

**Duration matched hedge**

A risk offsetting position constructed from a long position in one instrument, such as a government bond, and a short position in another instrument, such as an interest rate swap, which may have a different maturity, coupon, yield to maturity and equivalent life to the first but which has an equal and opposite duration.

**Embedded option**

An option implicit in another instrument. The commonest are: call options embedded in bonds, which allow the issuer to redeem the bond early; the options implicit in bonds with sinking funds; the embedded put provisions in some bonds, that allow investors to put the bond back to the issuer at a predetermined price; the caps in capped FRNs; the equity call options in convertibles and exchangeables; the mortgagee's prepayment options in mortgage-backed bonds; the options represented by attached debt or equity warrants; the currency options in dual-currency bonds and the debt or interest rate options in pay-in-kind bonds. Embedded currency, commodity, equity and interest rate options have become commonplace in both the private and public debt markets.

**Exchange-traded contract**

A futures or option contract traded on an organized exchange by exchange members. Exchange-traded contracts tend to be short-term, standardized and limited in complexity though innovation is changing this.

**Extendible**

Used of instruments whose life can be extended beyond an original term at the option of one or both of the counterparties. See extendible swap, extendible floater.

**Factor sensitivity**

The impact on a portfolio of assets of movements in the underlying risk parameter of an individual asset.

**Fair**

The fair price is usually either the theoretical price an instrument should fetch or the no-arbitrage price.The fair price of a future or forward contract is the price at which arbitrage between the derivative and the underlying asset just breaks even. The fair value of an option is what should be the price of that option in an efficient market with reference to theoretical option models.

**Floored**

The payout of options, warrants or swaps is floored if it is guaranteed to be at least a minimum specified amount. The opposite of capped.

**Forward-forward [interest] rate**

An interest rate that will apply to a loan or deposit beginning on a future date and maturing on a second future date. For example, a 6s/12s forward forward is an interest rate agreement fixing the rate payable on a loan starting in six months time and maturing six months later. Two forward-forward rates are used to calculate an FX forward-forward swap.

**Forward outright rate**

The actual forward exchange rate used in a forward contract. The forward foreign exchange rate for two currencies assuming simple interest rates can be expressed by: Ft = St * [1 + (rd x T - t) x 1/Dd] / [1 + (rf x T - t) x 1/Df] where Ft = the forward rate St = the spot rate (direct quotation) rd= the domestic interest rate rf = the foreign interest rate Dd= the daycount in the domestic currency Df= the daycount in the foreign currency T = the maturity of the forward contract t = the current time such that T - t = the life of the forward. (Note: rd and rf are spot i.e. zero coupon interest rates. For indirect quotations the foreign currency interest rate would be the numerator and the domestic currency rate would be the denominator.) The formula is the result of interest rate parity, the theory that states that investors will transfer funds from low-interest currencies to high-interest currencies until the advantage of doing so the interest rate differential is offset by the cost of covering the exchange risk in the forward market - that cost being the forward exchange margin. That is, the ratio of the forward rate to the spot is a reflection of the interest rates in the two countries.

**Forward points**

The number added to or subtracted from the spot exchange or interest rate to calculate a forward price, adjusted for point size convention. For example 100 forward points in USD/DEM is equal to DEM0.01 per USD. See swap rate.

**Futures contract**

An agreement to buy or sell a given quantity of a particular asset at a specified future date at a pre-agreed price. Like forwards, futures differ from options in that they represent an obligation to buy or sell the underlying. Unlike forwards, they have standard delivery dates, trading units and terms and conditions. They are available on a wide range of financial and commodity assets, generally expire quarterly and can be cash or physically settled. Most importantly, they are traded on exchanges which act as counterparties to all transactions and which run margining systems. Margin is the collateral futures traders must set aside against their positions. First, an initial margin must be deposited with the clearing house on entering a trade. Thereafter futures positions are marked-to-market daily and a variation margin is paid/received to maintain the required level of collateralization. The role of the exchange and the margin system significantly limit credit risk.

**Hedge**

To offset the potential risks and returns of one position by taking out an opposing position to create an outcome of greater certainty.

**Hybrid**

An instrument whose returns depend on a combination of risk types or which has been constructed from several different instruments to produce returns which mimic those of another instrument. A common hybrid is the combination of interest rate or currency swaps and barrier or digital options on other asset classes. See commodity-linked interest rate swap, hybrid barrier option.

**Implied forward rate**

A forward interest rate that can be implied from the par or zero coupon yield curves. Not only do the expectations embedded in the yield curve indicate what the yields on varying maturities of fixed-income instrument should be, they contain all the information needed to calculate, say, the one-year rate in one year's time from the two-year rate and the one-year rate.
So, if six-month Libor is 5.00% (180 days) and three-month Libor is 4.00% (90 days) the implied rate for three-month Libor in three months' time must be 6.01%, since this rate satisfies the condition that an investor {borrower} would be indifferent between receiving {paying} 4.00% for three months and reinvesting {rolling over} at 6.01% for a further three months, and receiving {paying} 5.00% for six months. The curve plotted by these rates, known as the implied forward curve, is steeper than the yield curve. That is, when the yield curve is positive, implied forward rates are higher than spot rates and in a negatively sloped curve implied forward rates are lower than spot rates. Mathematically:
(1 + r0,1 t0,1/D) (1 + r1,2 t1,2/D) = (1 + r0,2 t0,2/D) where r1,2 is the implied forward rate. The implied forward curve is central to an understanding of derivative products as they are priced off it, rather than the spot rate even if they are struck with reference to the spot. Therefore by definition, when using derivatives to profit from a market view, potential users must first compare their view with the implied forward. If they are the same, there is no opportunity to profit from that view. A number of derivative instruments have been devised that modify the payout from their vanilla versions by allowing users to take advantage of a view that differs from the implied forward, for example the Libor in arrears swap. Implied repo rate: The short-term financing rate that will make a cash-and-carry arbitrage involving the cheapest-to-deliver bond break even. It is equal to the return earned by buying the cheapest-to-deliver bond for a bond futures contract and selling it forward via a short position in the futures contract.

**Leverage**

The ability to control or gain exposure to a large nominal amount of an underlying asset with a relatively small amount of capital. Futures and options are leveraged because with relatively small down payments (of margin or premium) the buyer gains exposure to large amounts of the underlying.

**Leveraged**

When used for derivatives or structured notes 'leveraged' indicates that the instruments payoff formula includes a greater than one multiple of some underlying index or asset price. In the case of leveraged notes this is generally achieved using embedded swaps or options whose notional principal is greater than the nominal principal of the bond. See leveraged swap, leveraged diff floater, leveraged floater, total return index notes.
The New York Federal Reserve has defined leveraged derivatives transactions (LDTs) much more broadly as a derivative transaction (i) in which a market move of two standard deviations in the first month would lead to a reduction in value to the counterparty of the lower of 15% of the notional amount or $10 million and (ii) for notes or transactions with a final exchange of principal, where counterparty principal (rather than coupon) is at risk at maturity, and (iii) for coupon swaps, where the coupon can drop to zero (or below) or exceed twice the market rate for that market and maturity, and (iv) for spread trades that include an explicit leverage factor, where a spread is defined as the difference in the yield between two asset classes. This definition bears no strict relevance to the general concept of leverage but means the reclassification of many previously plain vanilla transactions as LDTs.

**Mark-to-market**

The process of determining the present market value of a security or derivative position. See market contingent credit derivative, mark-to-market swap, mark-to-market cap, swap guarantee.

**Margin**

See futures contract.

**Market risk**

The risk of mark-to-market losses associated with portfolios of financial instruments.

**Monetization**

In derivatives markets monetization refers to the realization of the value of the options embedded in puttable and callable bonds. This can be done using forward swaps or by selling call options on government bonds. Most commonly though swaptions are used. The issuer of a callable bond has in effect bought a receiver swaption with a notional principal equal to the bond principal, an exercise date equal to the call date of the bond and with the underlying swap maturity equal to the maturity date of the bond. Selling this swaption monetizes the value of the call feature.

**Naked**

The opposite of covered. A long or short derivatives position initiated without any corresponding position existing in the underlying. So, naked positions would include being long puts without an underlying position to hedge or being long a swap with no underlying liability or a smaller liability portfolio than the notional principal of the swap.

**Net present value (NPV)**

The difference between the present values of two different cashflows. For example, because there is no upfront premium payable on a standard interest rate swap, the present value at initiation of the future fixed- and floating-rate payment streams due under the swap must be equal hence the NPV is zero.

**Notional principal [amount]**

The nominal value used to calculate the cashflows on swaps and other cash-settled derivatives. In an interest rate swap, for example, each period's interest rates are multiplied by the notional principal amount and the daycount to determine the actual amount each counterparty must pay. In interest rate swaps the notional amounts are not exchanged, so any credit risk is limited to the net amount payable plus a potential future exposure factor. Descriptions of the size of the derivatives market almost always refer to notional principal amounts when in fact the amount of money at risk is a tiny fraction of that.

**Novation**

The replacement of one or more derivative contracts with new ones, often also with one of the counterparties replaced by a new one. One common use of novation is in the creation of chains of swaps which, having been cancelled and reassigned, can be used to provide loans in circumstances where straightforward lending would be expensive or not permitted.

**Off-market**

Below or above the market rate.

**Operational risk**

Any risk that is not market risk or credit risk related. This includes the risk of loss from events related to technology and infrastructure failure, from business interruptions, from staff related problems and from external events such as regulatory changes.

**Over-the-counter**

The market for securities or derivatives created outside organized exchanges by dealers trading directly with one another or their counterparties by telephone, screen, telex or other computer-driven means.

**Par swap yield curve**

The term structure of swap rates, that is, a yield curve that plots swap rates against maturity and that is derived from the zero-coupon yield curve.

**Par yield curve**

The curve formed by the yields to maturity associated with bonds currently selling at par. The par curve is important as the yields on bonds selling at par are likely to be more representative of the underlying term discounting rates implicit in the market. Bonds selling at a substantial discount or premium to par are often subject to special forces which distort their prices. For example, a high-coupon bond may be considered an especially desirable investment in an environment where interest rates have bottomed out. Gaps in the curve caused by a lack of available bonds are filled by interpolating from existing bonds the coupons necessary for bonds at those maturities to be priced at par.

**Parallel shift**

A parallel shift in the yield curve, assumed by many hedging strategies, is a movement of each point on the yield curve by the same amount at the same time.

**Participating derivative**

Derivatives that allow the holder to buy participation in the upside of the instrument either by giving up protection on the downside or by limiting the upside of products that in their vanilla form have unlimited profit potential. See participating forward, participating swap.

**Power derivative**

Applied to any structure that incorporates leverage that is unusual either on account of its magnitude or non-linearity. The most common form is an option whose payout is a power (usually the square) of the intrinsic value at maturity. See power libor swap, power option.

**Quanto**

A currency-protected derivative product that is, one denominated in a currency other than that of the underlying to which exposure is sought. The name refers to the variable notional principal of these products which reflects the fact that the face amount of currency coverage they contain rises or falls to cover changes in the foreign currency value of the underlying. An example is a EUR/USD option with a payout in Japanese Yen embedded in a Japanese yen deposit. See currency protected.

**Quantize**

To give a derivative quanto features. See currency protected.

**Ratchet**

Used for a variety of derivative structures in which key variables such as strike price are resettable, usually in an assymetrical manner. In some cases this leads to investors' gains being locked in regardless of future movements in the underlying asset. See ratchet floater.

**Second generation structured assets**

Bonds and notes incorporating design complexity in addition to simple embedded options. These include notes containing index maturity to reset frequency mismatch (such as a CMT FRN with coupons linked to 10-year Treasury rates but that are reset and paid on a quarterly basis), notes that pay a coupon based on the differential or sum of a number of indices, notes that include embedded exotic options, notes incorporating quantization and notes containing very highly leveraged formulae.

**Short-rate volatilities by mean reversion**

short rates tend to be pulled back towards a long-term average. The volatilities of each spot rate are modelled to produce a term structure of volatility - that is volatility plotted against term to maturity. This is an important input into term structure pricing models. The term structure of volatility is also sometimes a reference to the differing implied volatilities of options with different maturities. The implied volatilities of short-dated options change faster than those of longer-dated options. Volatility itself also exhibits mean reversion.

**Spot rate**

In currency markets, today's market exchange rate for a transaction now with standard immediate delivery (usually two business days after trade date). In interest rate markets, the spot rate is the rate at which a single future payment is discounted back to the present. That is, where observable, the n-year spot rate is the yield to maturity of a zero coupon bond with a maturity of n-years. For maturities at which zero coupon bonds are not available, the spot rates can be bootstrapped from coupon paying bonds at those maturities since the price of these bonds is the present value of all their cash flows with each cash flow discounted at the appropriate spot rate. See bootstrap.

**Spot yield curve**

The curve that plots spot rates against term to maturity.

**Spread**

The difference between the yields or volatility on two financial assets (aside from the bid-offer). For example, in the oil markets, the crack spread is the spread between the price of crude oil and the refined ('cracked') distillates such as gasoil and naphtha. In fixed income markets the credit spread is the difference in yields between fixed-income instruments of different credit qualities.In the options markets an option spread, sometimes just called a spread, is the purchase of one or more options and sale of others on the same underlying.

**Spread trade**

In derivatives either a trade designed to profit from movements in the spread between two or more underlying indices or an options trade involving the simultaneous purchase and sale of different options on the same underlying.

**Step-up {-down}**

A general concept that can be applied to any of the terms of a contract which determine the size of payments but not their timing, step-up or step-down features involve a schedule of values indexed in time which determine how payments will vary. So a bond with a step-up or step-down coupon will have a schedule of coupons which increase or decrease over time. Similarly a step-up or down barrier option is a barrier option whose barrier increases or decreases over time.

**Stepped**

When used for bonds denotes a bond with a fixed first coupon which then reverts to a predetermined floating rate formula. Differs from a step-up coupon in that only the first coupon acts as a step. Usually this first coupon is extremely attractive in comparison with vanilla FRN rates and is an encouragement to the investor to buy highly structured assets that take strong directional views. For example, leveraged inverse floaters and leveraged floaters often have a fixed first coupon.

**Structured note**

Bonds/notes whose performance is linked to that of a conventional security and an embedded derivative. Also known as embeddos, derivative-linked securities.

**Swap rate**

(i) The yield to maturity of the swap. That is, the price of the swap which, when used both as a fixed-rate payment and an internal rate of return, will equate the present value of the two payment streams. On a vanilla interest rate swap, the bid swap rate is the fixed rate a marketmaker will pay to receive Libor and the offer is the fixed rate a counterparty must pay to receive Libor. Swap rates are mathematically equal to the weighted average of all relevant FRAs and so are determined by the term structure of interest rates, credit and transaction costs. (ii) In currency markets, the swap rate is the forward points on a currency rate that is, the adjustment to the spot exchange rate that has to be made to compensate for interest rate parity differences between currencies. When it refers to the difference between spot and forward foreign exchange rates the swap rate is also known as the forward exchange margin.

**Swap spread**

The difference (positive) between swap rates and the relevant government bond market. The spread reflects the credit differential between the swap and government markets but in practice is also heavily influenced by supply and demand factors in the swap market. A glut of fixed payers will widen the spread. A glut of swapped new issuance will reduce it. The spread in any individual transaction will also be affected by the relative credit qualities of the counterparties to the transaction: a triple-A bank marketmaker will quote a wider swap spread to a single-B corporate than to a double-A supranational entity.

**Synthetic**

In financial contexts used for any instrument constructed from others so that its cashflows and sometimes risk-reward characteristics replicate those of another asset or liability. Such instruments are created either because certain users cannot buy the components separately or because an arbitrage opportunity allows the synthetic to be purchased {sold} more >cheaply {expensively} than the straightforward product. Almost any position or instrument can be constructed in this way. For example: a synthetic call option can be constructed by the simultaneous purchase of a put option and the underlying; a synthetic put from a long call and short position in the underlying; and a synthetic forward from a long European-style call and short European put with the same expiration and strike price. See conversion [arbitrage], put-call parity, static replication, synthetic forward, delta hedging.

**Systemic risk**

The risk that derivatives permit the transmission of risk across previously unrelated markets, thus making it more likely that a large shock in one will be transmitted (with negative consequences) to others. The term is also used for the risk supposedly inherent in the concentration of derivatives business at a small number of large financial institutions. If - so the argument runs - one of these were to fail, the whole financial system would be threatened.

**Term structure**

The interrelationship of underlying assets of different maturities.

The term structure of interest rates is the interrelationship of interest rates of different maturities.

It relates spot rates to the term to maturity in the form of the spot or zero coupon yield curve.

Modelling the relationships between spot rates at different points in the curve is crucial to the pricing of interest rate derivatives since even a short-term instrument will span several spot rates and so its price will depend on how they interact with each other and the rest of the term structure.

The dynamic nature of the term structure has led to the development of multi-factor pricing models where the factors represent changes in the level, slope and curvature of the term structure.

The term structure of volatility is the volatility of the prices or rates of the underlying at different maturities.

For example, studies of the term structure of interest rates show that spot rates at different maturities have different volatilities.

A basic observation is that long rates are less volatile than short rates and that long-rate volatilities are linked to current.

**Termination**

Cancellation of a risk management agreement or derivative transaction upon an agreed event and on previously agreed terms and conditions.

**Total return**

All the cashflows and capital gains or losses associated with an investment.

**Transaction risk**

The currency risk incurred by an entity with certain or near-certain cashflows in currencies other than the domestic accounting currency of the entity.

**Trigger**

See barrier, capped call [option], trigger forward.

**Value at risk (VAR)**

A measure of the maximum potential change in the value of a portfolio of financial instruments with a given probability over a specified time period.

**Yield curve**

A plot of interest rates versus time.

**Zero-coupon yield curve**

The spot rate curve of the observed or interpolated yields to maturity of default-free zero coupon bonds plotted against maturity. From this a forward rate curve or forward term structure can be implied to give the markets current expectation of future spot rates.