Numerix Glossary

Adaptive (sequence)

A sequence that adjusts to feedback on the fly to more accurately price a deal.

Analytic pricer

A method that derives the value of an asset directly from the input parameters without the use of numerical methods.

Antithetic Variates

A technique for improving Monte Carlo simulations by adding a mirror-image point q for every random point q in a random series.


Bilateral credit valuation adjustment.

Bilateral credit valuation adjustment (BCVA)

Adjustment to the price of a financial instrument due to the possibility of default by either counterparty.

Black-Derman-Toy model

A one-factor interest-rate model where the log of the short rate is a normal variable. Equivalent to the Black-Karasinski model without reversion. See also Black-Karasinski model.

Black-Karasinski model

A one-factor interest-rate model where the log of the short rate is a mean-reverting normal variable.

Black-Scholes model

An options-pricing model that follows geometric Brownian motion. Numerix uses the term to include the Black-Scholes partial differential equation, the exact pricing formulas, generalizations to time-dependent rates and volatility, tree-based methods for pricing analytically intractable instruments, and related features.


An aggregate view of a portfolio of trades, potentially across several underlying assets and/or asset classes.

Brace-Gatarek-Musiela/Jamshidian model

A multifactor term structure model where forward Libor rates are the underlying stochastic variables. Versions of the model differ in accordance with the chosen numeraire and the underlying rate modeled.

Class definition

An object that allows a user to create a new type of object, by combining a number of Numerix objects and defining their inputs.

Control variates

In Monte Carlo simulations, a variable whose value can be calculated both explicitly and also in the simulation; the known value is used to adjust the simulation, providing better values. See also variance reduction.


Considerations that narrow the definition of an underlying asset: trading calendar, day count, holiday calendar, etc. 

Credit valuation adjustment (CVA)

A quantitative measure of unilateral counterparty credit risk. CVA is a credit applied to the price of a derivative to reflect the cost of hedging the counterparty risk.

Curve interpolation

A calculation of the value between known points in order to approximate the value between points that are not in the initial data set.


Credit valuation adjustment.

Debit valuation adjustment (DVA)

A quantitative measure of unilateral counterparty credit risk. DVA is the credit applied to the price of a derivative as viewed from the counterparty's perspective.


Objects that are required to be created before the creation of a specific object.


Known with certainty; not stochastic. Variables are either deterministic or stochastic.


The number of random numbers needed for one path in a Monte Carlo simulation. It is equal to the number of factors times the number of time steps.


Debit valuation adjustment.


Expected positive exposure.


Expected tail loss.


An object containing date schedules used to define accrual periods and relevant fixings for a deal.

Expected positive exposure (EPE)

The time-weighted average of individual expected exposures for given forecast horizons.

Expected shortfall

A function of two parameters: N (the time horizon in days) and X% (the confidence level). It is the expected loss during an N-day period, with the condition that the loss is greater than the Xth percentile of the loss distribution.

Expected tail loss (ETL)

The expected loss at given low probability scenarios in VaR analysis.


An independent stochastic variable underlying a model. See also state variable.

Forward volatility

A volatility defined as of some forward time. Note that the volatility can be either instantaneous or term. See also instantaneous volatility, term volatility.

Historical volatility

The volatility of an underlying asset as calculated by actual measurement over a period of time. See also implied volatility.

Ho-Lee model

A one-factor interest-rate model where the short rate is a normal variable. This is equivalent to the Hull-White model without reversion. See Hull-White model.

Hull-White model

An interest-rate model where the short rate is a mean-reverting normal variable.

Implied volatility

The volatility of an option implied by the market price of a non-linear derivative. See also historical volatility, instantaneous volatility, term volatility.

Importance sampling

A method which places deviates where they are more useful by using information from the function.


(of N stochastic variables) Not completely describable by M variables, where M is less than N. Two stochastic variables may be independent even if they are correlated.

Index object

An application object representing the definition of an index used as a component in the building of a deal. An index object exists independently of any deal, and its definition is necessary for projection.

Instantaneous volatility

The volatility of a stochastic parameter appropriate for an infinitesimal time. This is the volatility used in most standard models—e.g., Hull-White. See also term volatility, forward volatility.

Kernel pricer

An object that groups together all objects needed to calculate the price of a user-defined trade.


The London interbank offered rate published on each London trading day. It reflects the reported interest rate for unsecured lending between banks in the London money market. In Numerix analytics, Libor is the generic name for simple cash rates used in fixing deals.


A security whose value is almost surely positive. It is a mathematical object used to define the probabilities for calculating expectation values.


A specific instance of a class.


In a Monte Carlo simulation, a single instance of all stochastic variables used in the simulation.

Positive definite matrix

A matrix whose eigenvalues are all positive and not zero.

Positive semi-definite matrix

A matrix whose eigenvalues are all positives or zero.

Potential future exposure

The maximum expected credit exposure over a specified period of time calculated at some level of confidence. The measure is used within the context of Counterparty Risk and is a part of the Basel 3 requirements.


Generated by a process that approximates a random distribution over a large number of occurrences.


Effectively the inverse of a cumulative-density function. Value at Risk is a quantile for a given confidence level.

Range accrual

A financial derivative of which a buyer would receive a payout pending the underlying asset trades within a predefined range. The payout is typically determined by the number of days within the range (n) divided by the number of days of the structure (M) multiplied by the pre-defined payout amount.

RMS error

Root-mean-square error.


The process of working values back through a tree from some future time to an earlier time, making use of the tree probabilities.

Root-mean-square error (RMS error)

A description of the width of the distribution of answers determined by a Monte Carlo method and the exact answer.


The language-based method that is used to describe the mechanics of a deal or structure.


A number (generally an integer) used to generate a pseudorandom sequence.

Simulation object

A Numerix object that stores information about a simulation. This information includes both random sequences generated by the simulation and random values calculated by the user.


A tree object containing value (asset, event, etc.) information for all possible sets of state variables at a point in time in the tree.

Smart conventions

A device for automatically looking up standard market parameters or conventions by providing the type of the instrument and currency. Usually smart conventions in CrossAsset XL are specified in the dependency conventions spreadsheet Conventions.xls but can be created and customized by the user.


1) An extensive selection of Excel examples supplied with CrossAsset and accessible via the Quick Start tool.

2) The custom deal workbooks a user can construct using the Solution Builder tool.

3) A set of frequently asked questions and answers available via the Numerix Support self-help portal.

Solutions workbook

A pre-built workbook in Numerix LiquidAsset XL that allows immediate pricing of a deal. It includes reports and any dependent data required by the sample deal.


The state of the world in a particular model, usually expressed as one or more variables, called state variables. For example, a state in a particular FX model might consist of an exchange rate and two short rates.

State variable

A parameter used to define the state of the world, often (but not necessarily) stochastic.

Sticky delta

Delta calculated under the assumption that the present value of future continuous dividends remains unchanged as the spot value changes. In FX markets, sticky delta would imply that the ATM implied volatility remains unchanged as the underlying Spot price changes.


Not known with certainty, random. Variables are either deterministic or stochastic.

Stratified sampling

Similar to Monte Carlo simulation, which tries to distribute variates evenly by subdividing the domain into subregions.

Term volatility

The constant volatility value of a stochastic parameter appropriate for a finite period of time. Term volatility can be either spot or forward. See also instantaneous volatility, forward volatility.

Time series

An ordered sequence of numbers—for example, daily closing prices of a stock.


In the kernel pricer, a record of the calculations performed on each fixing date—the action that occurs for each event.

Variance reduction

A general name for several techniques designed to improve the accuracy of a Monte Carlo or quasi-Monte Carlo simulation without simply increasing the number of paths in a run.

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