• Back-testing

    The validation of a model by feeding its 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.

  • 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. 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.

  • Basis

    1. The difference between the price of a futures contract and its theoretical value.
    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 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.

  • 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 a floating leg is based on the returns on a basket of underlying assets, such as equities, commodities, bonds, or swaps. The other leg is usually (but not always) a reference interest rate such as Libor, plus or minus a spread.

  • 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.

  • Bermudan option

    The holder of a Bermudan option, also known as a mid-Atlantic option, has the right to exercise it on one or more possible dates prior to its expiry.

  • Best-of option

    A best-of option pays out on the best performing of a number of underlying assets over an agreed period of time. For instance, if a basket contains stock A, stock B and stock C and stock B gains in value by the larger amount during the products term, then the payout would be based on the increase in value of Stock B.

  • Beta

    1. The beta of an instrument is its standardised 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.
    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.


  • 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.

  • 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.

  • 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 (ie 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_and_rsquo;s strike price, the price of the underlying, the option_and_rsquo;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.

  • Bond

    Companies or governments issue bonds as a means of raising capital. The bond purchaser is in effect making a loan to the issuer, and unlike with shares investors at no point hold a stake in the company.

  • 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.

  • 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.

  • 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.

  • Butterfly spread

    The simultaneous sale of a straddle and purchase of a 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 capitalise 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 (ie 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).

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