Glossary
Accounting-based credit models Models that measure credit risk based on an analysis of financial ratios.
Additive value function A type of multicriteria evaluation model where the overall performance of an available option is obtained as a weighted sum of partial performance assessments. It is a compensatory model, in which the weak performance on one dimension can be compensated by strong performance on others.
Akaike Information Criterion (AIC) A measure of the quality of a statistical model for a given dataset allowing for selection of the best model.
Asset/liability management A risk-management process used by financial institutions to manage their assets and cash flows in accordance with their obligations (liabilities).
Banking stability index An index that describes the degree to which a banking system as a whole can withstand the financial distress of some financial agents.
Basel accords A set of international standards issued by the Basel Committee on Banking Supervision, with a strong focus on the capital adequacy of banks.
Beta The relative risk of an asset in comparison to the market or other defined benchmark.
Budget constraint Restriction that the sum of a set of investment weights equals the investor's budget, which is usually normalized to one.
Bulk volume classification A common method used to classify a trade as either buyer-initiated or seller-initiated.
CEO Chief executive officer, usually the most senior corporate officer managing a corporation.
CFO Chief financial officer, reports to CEO and the board of directors.
Cholesky decomposition A decomposition of a negative (positive) semi-definite matrix into a lower triangular matrix, a diagonal matric of Cholesky values, and the transpose of the lower triangular matrix. This decomposition can be used to impose concavity (convexity) on a function.
Class actions Collective lawsuits in which there is a group of people in similar circumstances suing another party in order to be compensated.
Classification technique A technique in which a new observation will be classified into a set of categories (sub-populations). The problem bases on a training set of data containing observations whose category membership is known.
CMR A multiperiod PD rate, structurally equivalent to pricing EPE as the contingent leg of a CDS, by applying the counterparty spread to it.
Conditional distress probability The probability that given the distress or bankruptcy on one specific agent, another financial agent comes under financial distress as a consequence.
Conditional Value at Risk CVaRα (at the confidence level α) is a coherent risk measure defined as the mean of the α-tail distribution of losses.
Contamination bounds Upper and lower bounds for the optimal performance of the objective constructed for purposes of stress testing.
Copula models Mathematical models which formalize the joint and conditional distress probabilities.
Counterparty credit risk measurement and management (CCR) exposure Quantifies how much money the counterparty might owe the bank in the event of default.
Covariance matrix Square symmetric matrix in which elements in the leading diagonal are the asset variances. Entry in row i column j is the covariance between returns on assets i and j, respectively.
Covariance specification tests A set of statistical tests for assessing the performance of various covariance specifications in the context of multivariate GARCH-type models.
Credit default swap (CDS) A bilateral agreement between counterparties to insure against the loss of risky reference debt.
Credit ratings Classifications of obligors into credit risk categories, prepared either internally by a credit institution or provided externally by credit-rating agencies.
Credit risk The risk due to the failure of an obligor to meet scheduled debt obligations.
Credit scoring The process of evaluating and scoring the creditworthiness of obligors, usually based on quantitative models.
Credit valuation adjustment (CVA) The product of the EPE times the LGD times the CMR.
Current exposure (CE) Measures the exposure if the counterparty were to default today.
Cut-off point It is the higher value an observation can take in order to be categorized categorized to a predefined group (e.g., CA/NSCA group).
Delinquent loans Loans with repayments more than thirty days overdue.
Distance to default A numerical indicator describing the danger of default in the next period of a firm. This indicator is related—but not identical—to the probability of default in the next period.
Directional output distance function A function that seeks the maximum expansion in desirable outputs and contraction in undesirable outputs.
Economic capital (EC) The difference between a UL measure, or some extreme loss at some confidence level (e.g., a high quantile of a loss distribution) and the associated EL measure.
Efficient portfolio A portfolio of assets with the highest possible return for a given level of risk or with the lowest risk for a given level of expected return.
Efficient frontier A concave curve, which relates the expected return on efficient portfolios to their volatility.
Efficient portfolio A portfolio, which has the minimum variance (or, equivalently, volatility) for a given level of expected return; alternatively, the maximum expected return for a given level of variance (or volatility).
Energy trading Exchange of contracts for buying and selling electricity in a regulated market or in an OTC market.
Eigenvector A vector that when a square matrix multiplies this vector, it yields a constant multiple of the vector.
Expected loss (EL) A measure generally thought of as some likely loss measure over some time horizon (e.g., an allowance for loan losses amount set aside by a bank).
Expected positive exposure (EPE) The average of a simulation of a large number (on the order of 102 to 103) different paths for the various underlying future prices in the possible market environments.
Expected return The expected value of the portfolio return.
Exposure-at-default (EAD) The economic exposure on a claim to a counterparty that defaults.
External ratings A credit rating provided by an independent rating firm.
Financial system The universe of all financial agents of a country (central bank, private and governmental banks, and other financial intermediaries as, e.g., insurance companies) with all the interdependencies, as mutual share holdings and mutual loans.
Firm value models Mathematical models describing the future development of the value (assets minus liabilities) of a firm using stochastic variables.
Fixed transaction costs Transaction costs that are charged independently of the amount of capital invested.
Forward market Special financial contracts that allow hedging against future movements of the price of a commodity or of a financial activity.
Forward zero curve The forward spread curve between a rated bond and the risk free rate on a zero coupon bond.
Futures contract An agreement between two parties to perform a transaction for an asset in the future with pre-agreed terms (date of the transaction, its volume, and price).
GARCH models Generalized autoregressive conditionally heteroskedastic models. Statistical models describing the conditional variance of a random variable, mostly times series of returns on speculative assets.
Hedonic prices A method of obtaining the price of a single characteristic from a good or service that consists of a bundle of characteristics.
Heteroskedasticity Subpopulations within a data set have different variability across groups.
Hierarchical Bayesian model A model that allows researchers and practitioners to develop more realistic models in decision making. The promise of Bayesian statistical methods lies in the ability to deal with problems of high complexity.
High frequency trading The use of computational algorithms and electronic systems to perform financial transactions rapidly in investment strategies that seek to make short-term profits.
Hypergeometric functions Special functions that are solutions of second order linear ordinary differential equations. These are usually infinite series.
i.i.n.d Independent and identical normal distribution.
Individual distress probability The probability that one specific financial agent suffers distress in the next period.
Integrated method A method of bringing together two systems into one, on the basis that the new one will deliver better classification results.
Joint distress probability The probability that a given group of financial agents all suffer distress in the next period.
Kurtosis A measure of the peakedness of the distribution of a random variable.
Leptokurtosis A random distribution with higher kurtosis than a normal distribution as there is a greater concentration of observations around the mean.
Linear programming (LP) model An optimization model where constraints and objective function are linear.
Logistic regression A regression that measures the relationship between a categorical dependent variable and one or more independent variables.
Loss cascade Due to interrelations between financial agents, the default of one may cause the default of others in a cascading series, like falling dominoes.
Loss-given-default (LGD) The ultimate economic loss on a claim to a counterparty that defaults.
Market portfolio A portfolio consisting of all assets in a market, with each asset weighted in proportion to its market value relative to the total market value of all assets.
MCDA Multicriteria decision aid models that consider multiple criteria in decision–making environments.
Mid-cap Companies with a medium-sized market capitalization.
Minimum variance portfolio A portfolio on the efficient frontier, which has the minimum possible variance.
Mixed-integer linear programming (MILP) model An optimization model where constraints and objective function are linear, and possibly some variables are constrained to take integer values.
Monte Carlo modeling The simulation of multiple random scenarios of asset returns.
Multicriteria decision aiding A field of operations research dealing with decision support in problems involving multiple conflicting decision criteria.
News impact curve A graphical representation of the degree of asymmetry of volatility to positive and negative innovations.
Nonperforming loan A loan that is past due more than three months, a loan to a borrower who is bankrupt, or a loan that is in the process of being restructured.
Nuisance parameters Parameters in a probability distribution which cannot be removed by standardization or transformation and thus confound statistical tests.
Output analysis Aims at analysis of the obtained results in connection with uncertainty or perturbation of input data.
Pay-out The expected financial return from an investment or the expected income/salary/bonus.
Polynomial chaos An approach to determine the evolution of uncertainty using a nonsampling based method, when there is probabilistic uncertainty in the system parameters.
Portfolio Amount of capital invested in each asset of a given set.
Portfolio optimization The process for defining the best allocation of capital to assets in terms of risk-return criteria.
Portfolio selection The process of constructing an efficient portfolio.
Potential exposure (PE) Measures the potential increase in exposure that could occur between today and some time horizon in the future.
Power capacity planning Planning for future development of plants to produce electricity.
Preference disaggregation analysis A methodological field in multicriteria decision aiding involved with the elicitation of preferential information from data using nonparametric regression techniques.
Probability of default The likelihood that an obligor will fail to meet scheduled debt payments in a given time period.
Probit regression A type of regression that aims to estimate the probability that an observation with particular characteristics will be classified into a predetermined category.
Quadratic utility function A utility function that is a quadratic function of its argument.
Ratings based models Models that incorporate credit ratings such as those provided by Standard & Poor's, Moody's, and Fitch.
Revenue function Maximum potential revenues that a firm can produce, given output prices and costs of production.
Regime-switching model A model with more than one state where the switching between regimes is governed by a transition matrix.
Regulatory capital (EC) The difference between a UL measure, or some extreme loss at some confidence level (e.g., a high quantile of a loss distribution) and the associated EL measure as dictated by a supervisory model.
Risk appetite A non-negative real number that describes an investor's appetite for risk, with higher values corresponding to a greater degree of aggression. The reciprocal is risk aversion.
Risk aversion The attitude of investors toward risk. Risk aversion is described by a concave utility function, risk-neutral investors have a linear utility function, and risk-prone investors have a convex utility function.
Risk constraints Prescribe the upper bound of the portfolio risk (expressed by means of a risk measure).
Risk-free rate A rate of return that is known for certain in advance and for which there is no default risk.
Risk measure Quantitative measure of the variability of losses or profits due to uncertain and undesired events.
Risk premium The extra return that investors require for risky investments over risk-free return.
Robustness analysis The examination of the validity of a solution and the results of an analysis to changes in the decision and modeling context (data, hypotheses, modeling assumptions).
Robustness test A test that investigates the degree to which a method/technique provides correct results in the presence of invalid inputs.
Safety measure A function, complementary to a risk measure, that measures the portfolio performance in terms of risk with respect to the expected return (level of safety of a portfolio). A safety measure has to be maximized when it is the objective function of a portfolio optimization model.
Second-order stochastic dominance Relationship between two random variables based on comparison of expected utilities for all non-satiate and risk-averse decision makers.
Security market line The tangent to the efficient frontier corresponding to the risk-free rate. All portfolios on this line consist of a holding in the market portfolio and a long or short position in the risk-free rate.
Self-financing portfolio A portfolio with both long and short positions for which the net investment required is zero.
Shadow output prices Unobservable price ratio that supports a given output mix and equals the opportunity cost of production.
Sharpe ratio The ratio of the expected excess return on a portfolio to its volatility.
Simultaneous confidence intervals A set of confidence intervals constructed with a specified overall probability.
Single-period portfolio optimization model An optimization model that provides the optimal portfolio at a given point in time for a single investment period.
Skewness A measure of the distributional asymmetry of a random variable.
SOX The Sarbanes–Oxley Act of 2002; an act intended intended to protect investors by improving the accuracy and reliability of corporate disclosures made pursuant to the securities laws.
Standard constants Three real scalars that determine the location, slope, and curvature of the efficient frontier.
Stationarity The property of a stochastic process with constant mean and variance where the covariance between two points in the process is determined by the distance between the two points.
Stein's lemma A mathematical result that plays an important result in portfolio selection.
Stochastic programming An optimization modeling approach for dealing with decision problems under uncertainty.
Stress testing The investigation of unexpected loss (UL) under conditions outside our ordinary realm of experience (e.g., extreme events not in our reference datasets).
Structural credit models Models that measure distance to default based on the debt and equity structure of a company and fluctuations in the market values of that company's assets.
Tangency portfolio A synonym for the market portfolio.
Tikhonov's regularization Robust solution of an approximate system of linear equations, taking into account the errors in the solution and its stability to changes in the problem data.
Time substitution Given a fixed amount of input that can be used over some range of time, time substitution is the process of choosing when and how intensively to use that input so as to maximize production.
Transaction costs Costs that are charged when a transaction (buying or selling) takes place.
Transition credit models Models that measure credit risk based on the probability of a borrower transitioning from one credit rating to another.
Transition probability matrix The probability matrix that governs the switching between regimes.
Trapezoidal rule A standard technique for numerical integration.
Unexpected loss (UL) A measure generally thought of as some unlikely loss measure over some time horizon (e.g., an allowance for loan losses amount set aside by a bank).
Utility function A nondecreasing and usually nonlinear function that maps an outcome to its importance. In portfolio selection, the outcome is usually return and the utility function is invariably concave.
Variable neighborhood search A metaheuristic approach for solving complex optimization problems (combinatorial and global optimization), which is based on the idea of improving a solution by systematically searching in distant neighborhoods of the solution.
Variable transaction costs Transaction costs that depend on the amount of capital invested.
Value at risk (VaR) The potential loss over a given time period for a selected level of confidence.
Volatility specification tests Statistical tests for assessing the performance of various volatility models.
Volume synchronized probability of informed trading (VPIN) A procedure used to estimate the probability of informed trading based on volume imbalance and trade intensity. VPIN quantifies the role of order toxicity (adverse selection risk in high frequency trading) in determining liquidity provisions.