BACK-TESTING
The validation of a model by feeding it historical data and comparing the model’s results with the historical reality. The reliability of this technique generally increases with the amount of historical data used.
BACKWARDATION
The situation when the cash or spot price of a commodity is greater than its forward price. A backwardation occurs when there exists insufficient supply to satisfy nearby demand in a commodity market. The size of the backwardation is determined by differences between supply/ demand factors in the nearby positions compared with the same factors on the forward position. There is no inherent limit to the backwardation, also referred to as a “back”.
See also
contango
BARRIER FLOATER
A floating-rate note in which the coupon is knocked-in or knocked-out if the reference interest rate exceeds or falls below a certain barrier level (see trigger+condition).
See also
range note
BARRIER OPTION
Barrier options, also known as knock-out, knock-in or trigger options, are path-dependent options which are either activated (knocked-in) or terminated (knocked-out) if a specified spot rate reaches a specified trigger level (or levels) between inception and expiry. Before termination knock-out options behave identically to standard European-style options, but carry lower initial premiums because they may be extinguished before reaching maturity. In contrast, knock-in options behave identically to European-style options only if they are activated/knocked-in and so also command a lower premium.
The standard barrier options have barrier levels that are monitored continually during the lifetime of the option. Single barrier options that have a barrier level above current spot are classified as up-and-out or up-and-in options. For single barriers below spot the usual terminology is down-and-out for the knock-out barrier option, and down-and-in for the knock-in barrier option.
An alternative terminology for single barrier options classifies barrier options where the barrier is out-of-the money with respect to the strike price as regular barrier options. In-the-money barrier options are further differentiated into reverse barrier options (for cases where the barrier may be breached as the underlying asset’s spot rate moves deeper in-the-money) and geared barrier options (examples where the barrier is in-the-money and lies between the strike and the underlying spot rate) A double barrier option has both an upper and lower barrier.
Many variations on the barrier theme are available. Barrier levels can be monitored continually, at discrete fixing times (discrete barrier options) or only at the final expiry date of the option (at-expiry barrier options). Barriers may be active only during distinct time intervals (window barrier options) or may change value at fixed points during the lifetime of the option (stepped barrier options). Barriers may need to be breached for a certain time before they are considered triggered (Parisian Barrier Options) or may allow for partial triggering depending upon how far beyond the trigger level the underlying asset is observed (Soft Barrier options). Barriers may reference a different underlying to that of the option itself – such barriers are known as outside barriers.
BARRIER RISK
The value and sensitivities (Greeks) of barrier options can be subject to large swings when the spot rate is at, or near, the trigger level. This is particularly true for reverse barrier options and geared barrier options, where the option has positive intrinsic value at the Barrier. The specific nature of these swings can make the management of such products riskier, hence barrier risk.
See also
stealth
BASEL CAPITAL ACCORD
The Basel Capital Accord was first issued in July 1988 by the Basel Committee on Banking Supervision, a panel of banking supervisory authorities established by the central bank Governors of the Group of Ten (G-10) countries in 1975. In April 1993, the Committee announced preliminary details of a package of supervisory proposals for applying capital charges to the market risk of banks. These proposals were centered on the use of a standardized “building-block” methodology, similar to the one eventually used in the European Union’s Capital Adequacy Directive.
After two years of industry comment, a revised version of the proposed Supplement to the Accord was released in April 1995. The main change was that banks could now calculate capital requirements using their own in-house models as an alternative to the standardized methodology, subject to their regulator’s approval. Following a second period of industry comment, the Committee issued the final version of the Supplement in January 1996, due for implementation by the G-10 supervisory authorities by the end of 1997. This version included the recognition of empirical correlations across broad risk factor categories.
The supplemented Accord specified both quantitative and qualitative requirements for in-house models. The crucial quantitative requirement is that banks should calculate 99th percentile value-at-risk every day, working with a holding period of 10 days and a historical observation period of a year. Furthermore, it was proposed that there would be additional charges for those banks whose models failed to perform adequately in historical back-testing or were felt to possess specific risk factors.
In June 1999 the Basel Committee formally released its long-awaited proposal for a new Capital Accord. This first consultative paper signaled a move towards using credit ratings rather than OECD status to set capital allocations. In January 2001 the second consultative paper was released. This new paper – dubbed Basel II – retained the 1999 proposal’s three-pillar approach that included minimal capital requirements, market discipline and supervisory review, but also included substantial additions. Three distinct methods for the calculation of minimum capital requirements were proposed.
Firstly, a standardized approach geared towards smaller banks was proposed. Exposures to different counterparties will be quantified in terms of risk weights based on assessments by external ratings agencies – with more sensitivity to ratings than in previous risk-bucketing plans.
For more sophisticated banks, two internal ratings-based (IRB) approaches to credit risk have been devised – the foundation and advanced – that allow greater use of banks’ own internal credit risk models. It is the Basel Committee’s intention to tailor regulations so that banks are encouraged to migrate towards the more sophisticated approaches, and that these new approaches bring regulatory capital more closely in line with the economic capital that banks calculate they should be holding, as determined by their own internal models.
Implementation of Basel II is due in 2005. Features of Basel II that have caused most discussion include the 20% operational risk charge, a 1.5 multiplication factor in the IRB risk weightings and the w charge for credit derivatives.
BASEL II
See
Basel Capital Accord
BASIS
1. The difference between the prices of a futures contract and the underlying.
2. The convention for calculating interest rates. A bond can be 30/360 or actual/365 in the US, or 360/360 in Europe. Money market instruments can be actual/360 in the US or actual/365 in the UK and Japan.
BASIS RISK
In a futures market, the basis risk is the risk that the value of a futures contract does not move in line with the underlying exposure. Because a futures contract is a forward agreement, many factors can affect the basis. These include shifts in the yield curve, which affect the cost of carry; a change in the cheapest-to-deliver bond; supply and demand; and changing expectations in the futures market about the market’s direction.
Generally, basis risk is the risk of a hedge’s price not moving in line with the price of the hedged position. For example, hedging swap positions with bonds incurs basis risk because changes in the swap spread would result in the hedge being imperfectly correlated. Basis risk increases the more the instrument to be hedged and the underlying are imperfect substitutes.
BASIS SWAP
An interest rate basis swap or a cross-currency basis swap is one in which two streams of floating rate payments are exchanged. Examples of interest rate basis swaps include swapping $Libor payments for floating commercial paper, Prime, Treasury bills, or Constant Maturity Treasury rates; this is also known as a floating-floating swap. A typical cross-currency basis swap exchanges a set of Libor payments in one currency for a set of Libor payments in another currency.
BASIS TRADING
To basis trade is to deal simultaneously in a derivative contract, normally a future, and the underlying asset. The purpose of such a trade is either to cover derivatives sold, or to attempt an arbitrage strategy. This arbitrage can either take advantage of an existing mispricing (in cash-and-carry arbitrage) or be based on speculation that the basis risk will change.
BASKET CREDIT DEFAULT SWAP
A credit default swap which transfers credit risk with respect to multiple reference entities. For each reference entity, an applicable notional amount is specified, with the notional of the basket swap equal to the aggregate of the specified applicable notional amounts. Types of basket credit default swaps include linear basket credit default swaps, first-to-default basket credit default swaps, and first-loss basket credit default swaps.
See also
credit default swap
BASKET OPTION
An option that enables a purchaser to buy or sell a basket of currencies, equities or bonds.
BASKET SWAP
A swap in which the floating leg is based on the returns on a basket of underlying assets, such as equities, commodities, bonds, or swaps. The fixed leg is usually (but not always) a reference interest rate such as Libor, plus or minus a spread.
BASKET TRADING
See program trading
BEAR SPREAD
An option spread trade that reflects a bearish view on the market. It is usually understood as the purchase of a put spread.
See also
bull spread
BERMUDAN OPTION
The holder of a Bermudan option, also known as a mid-Atlantic or semi-American option, has the right to exercise it on one or more possible dates prior to its expiry.
See also
option styles
BETA
1. The beta of an instrument is its standardized covariance with its class of instruments as a whole. Thus the beta of a stock is the extent to which that stock follows movements in the overall market. If a stock has a beta greater than one, it is more volatile than the market; if less than one, it is less volatile.
2. Beta trading is used by currency traders if they take the volatility risk of one currency in another. For example, rather than hedge a sterling/yen option with another sterling/yen option, a trader, either because of liquidity constraints or because of lower volatility, might hedge with euro/yen options. The beta risk indicates the likelihood of the two currencies’ volatilities diverging.
BETTER-OF-TWO-ASSETS OPTION
See
outperformance option
BID DATE
In a competitive bid transaction, the date on which swap Providers submit bids and the price/rate/agreement is established with the winning Provider.
BID PACKAGE
Documentation distributed by or on behalf of an Issuer to qualified Providers, detailing the terms, conditions and structure of the swap desired by the Issuer, which the Providers will use to formulate their bid on the scheduled bid date.
BILATERAL NETTING
Agreement between two counterparties whereby the value of all in-the-money contracts is offset by the value of all out-of-the money contracts, resulting in a single net exposure amount owed by one counterparty to the other. Bilateral netting can be multi-product and encompass portfolios of swaps, interest rate options, and forward foreign exchange.
BINARY OPTION
Unlike simple options, which have continuous pay-out profiles, that of a binary option is discontinuous and pays out a fixed amount if the underlying satisfies a predetermined trigger condition but nothing otherwise. Binary options are also known as digital or all-or-nothing options.
There are two major forms: at maturity and one-touch. At maturity binaries, also known as European binaries or at expiry binaries, pay out only if the spot trades above (or below) the trigger level at expiry. One-touch binary options, also known as American binaries, pay out if the spot rate trades through the trigger level at any time up to and including expiry. The pay-out of a one-touch binary may be due as soon as the trigger condition is satisfied or alternatively at expiry (one-touch immediate or one-touch deferred binaries). As with barrier options, variations on the theme include discrete binaries, stepped binaries, etc. Binary options are frequently combined with other instruments to create structured products, such as contingent premium options.
BINARY PAY-OUT
See binary option, credit default swap, exotic option
BINOMIAL MODEL
Any model that incorporates a binomial tree.
BINOMIAL TREE
Also called a binomial lattice. A discrete time model for describing the evolution of a random variable that is permitted to rise or fall with given probabilities. After the initial rise, two branches will each have two possible outcomes and so the process will continue. The process is usually specified so that an upward movement followed by a downward movement results in the same price, so that the branches recombine. If the branches do not recombine it is known as a bushy, or exploded, tree. The size of the movements and the probabilities are chosen so that the discrete binomial model tends to the normal distribution assumed in option models as the number of discrete steps is increased. Options can be evaluated by discounting the terminal pay-off back through the tree using the determined probabilities. Interest in binomial trees arises from their ability to deal with American-style features and to price interest rate options. For example, American-style options can readily be priced because the early exercise condition can be tested at each point in the tree.
BISTRO
BISTRO (Broad Index Secured Trust Offering), the synthetic securitization program developed by JPMorgan in 1997, is a structure that transfers tranched credit exposure to large, diversified portfolios of commercial or consumer loans from the securitizing bank to investors.
BLACK-DERMAN-TOY MODEL
A one-factor log-normal interest rate model where the single source of uncertainty is the short-term rate. The inputs into the model are the observed term structure of spot interest rates and their volatility term structure. The Black-Derman-Toy model, such as the Ho-Lee model, describes the evolution of the entire term structure in a discrete-time binomial tree framework. The model can be used to price bonds and interest rate-sensitive securities, though the solutions are not closed-form.
BLACK-SCHOLES MODEL
The original closed-form solution to option pricing developed by Fischer Black and Myron Scholes in 1973. In its simplest form it offers a solution to pricing European-style options on assets with interim cash pay-outs over the life of the option. The model calculates the theoretical, or fair value for the option by constructing an instantaneously riskless hedge: that is, one whose performance is the mirror image of the option pay-out. The portfolio of option and hedge can then be assumed to earn the risk-free rate of return.
Central to the model is the assumption that market returns are normally distributed (i.e., have lognormal prices), that there are no transaction costs, that volatility and interest rates remain constant throughout the life of the option, and that the market follows a diffusion process. The model has five major inputs: the risk-free interest rate, the option’s strike price, the price of the underlying, the option’s maturity, and the volatility assumed. Since the first four are usually determined by the market, options traders tend to trade the implied volatility of the option.
BLENDED INTEREST RATE SWAP
A technique that involves combining two interest rate swaps to produce a more attractive overall rate. It involves at least two transactions. For example, if a counterparty fixes its floating rate borrowing cost at 10% and rates go down to 8%, it may do another swap with the same counterparty at 8% and combine the two to create a rate closer to the market.
bma index
Formerly the PSA Municipal Swap Index; is the principal benchmark for the floating rate interest payments for tax-exempt Issuers. The BMA Index is a national rate based on a market basket of approximately 250 high-grade, seven-day tax-exempt variable rate demand obligation issues of $10 million or more. In November 2006, the Bond Market Association (BMA) merged with the Securities Industry Association to form the Securities Industry and Financial Markets Association (SIFMA). Officially, the BMA Index is now called the SIFMA Swap Index, but it is still widely referred to by market participants as the BMA Index.
See also
SIFMA Swap Index.
BOND FUTURE
A futures contract on a bond. The underlying can be of two types. The first is a notional (theoretical) bond, for example the 10-year government bond futures contract on Marché à Terme International de France (Matif), which has a notional seven- to 10-year underlying government bond with a 10% coupon. The second type is a futures contract on a specific bond, for example, the futures contract on the Danish government bond 8% 2000, listed on the Guarantee Fund for Danish Options and Futures. The notional type is more common.
The theoretical price of a bond futures contract equals the spot price of the underlying bond plus its net cost of carry. The higher the cost of carry (measured by its implied repo rate) for the cash bond, the more value there is in holding a futures contract instead, which is simply another way of buying a cash bond but at a future date. If the financing costs of holding a bond are lower than the bond’s yield, the bond will have positive carry and the futures contract will trade at a discount. If the financing costs of the bond are higher than the bond’s yield, the futures will trade at a premium. Hence bond futures normally trade at a discount to the cash in an upward-sloping yield curve and at a premium in a downward-sloping one. The degree of premium or discount will decrease the closer the futures contract is to expiry.
When futures are based on a notional bond, the exchange has to specify which bonds are deliverable into the futures contract. These can change periodically as outstanding issues get shorter and reach maturity. Because bonds have differing coupons, the exchange has to specify a conversion factor that allows those bonds to be compared on an equal basis to the notional underlying. A bond’s conversion factor is the value of one unit of that bond were it to trade at a yield to maturity equal to that of the notional bond. Because of demand/supply conditions, some bonds will be cheaper to deliver than others. The cheapest to deliver will be those where the greatest profit can be made from holding the bond and delivering it into the futures contract (called cash-and-carry arbitrage). This is dependent on the supply of bonds in the market, and on a bond’s maturity and coupon.
BOND INDEX SWAP
A swap in which one counterparty receives the total rate of return of a bond market or segment of a bond market in exchange for paying a money market rate. Counterparties may also swap the returns of two bond markets. The two most common indexes used to measure bond market returns are the JPMorgan government bond index and the Salomon Brothers world government bond index. Bond index swaps can be an attractive way of gaining exposure to a market if the investor wants to avoid the trouble and expense of buying individual bonds, bearing in mind there are currently no government bond index futures. Bond index swaps can also be used to pass on bond market exposure when an investor does not want to sell core bond holdings, either because of wide price spreads or because they were difficult to obtain.
There can also be tax advantages in using bond swaps. For example, in Japan, banks and securities houses are exempt from withholding tax, but most foreign investors are not. Banks can therefore pass on some of those tax advantages in the swap. Also known as a total rate of return swap.
BOND OPTION
An option offered on debt, usually government securities, although OTC options are available on corporate debt. The options can either be ex-change-traded, listed or OTC. Bond options have traditionally been standard European-style or American-style puts and calls. There is more interest in exotic structures such as yield curve options, inter-market spread options, and quanto options.
BOND WARRANT
See
warrant
BORROWING
Derived from “borrowing metal from the market,” which is achieved by buying a nearby date and simultaneously selling a date further forward.
See also
cash and carry
BOX
To buy/sell mispriced options and hedge the market risk using only options, unlike the conversion or the reversal, which use futures contracts. If a certain strike put is underpriced, the trader buys the put and sells a call at the same strike, creating a synthetic short futures position. To get rid of the market risk, he sells another put and buys another call, but at different strike prices.
BRACE-GATAREK-MUSIELA (BGM) MODEL
See
market model of interest rates
BREAK FORWARD/CAPPED FORWARD
A strategy that involves buying a synthetic off-market currency forward (buying and selling a put and a call at the same strike price) and the simultaneous purchase of another option, allowing a purchaser to benefit from favorable exchange rate movements. The transaction is usually constructed for zero cost because the premium from the off-market forward pays for the option.
BUILDING-BLOCK APPROACH
The building block approach to calculating capital adequacy is the basis for the quantitative requirements of the European Union’s Capital Adequacy Directive (CAD), as well as the standardized approach of the Basel Capital Accord. This approach recognizes to some extent the risk reduction that arises from offsetting positions, but treats individual market risks as additive, and further distinguishes between general market risk and specific risk, the latter reflecting risks specific to individual securities. Capital is charged as a percentage of the net face value of various positions, the percentage being a function of the type and tenor of security, and of the type of risk.
See also
comprehensive approach
BULL SPREAD
An option spread trade that reflects a bullish view on the market. It is usually understood as the purchase of a call spread.
See also
bear spread
BUTTERFLY SPREAD
The simultaneous sale of an at-the-money straddle and purchase of an out-of-the-money strangle. The structure profits if the underlying remains stable, and has limited risk in the event of a large move in either direction. As a trading strategy to capitalize upon a range trading environment it is usually executed in equal notional amounts.
Alternatively, such trades are often applied to benefit from changes in volatility. In such circumstances the butterfly spread is traded on a “vega-neutral” basis (i.e., the volatility sensitivity of the long position is initially offset by the volatility sensitivity of the short position). As the holder of an initially vega-neutral spread, the trader will benefit from changes in volatility since the strangle position profits more from an increase in volatility than the straddle and loses less than the straddle in a decline in volatility (this is due to the fact that the vomma of the strangle is higher than that of the straddle).