Quantitative finance & development glossary
182 definitions with examples. Study the related calculations in the curriculum or explore Python tools.
Ablation
A comparison that removes or changes one component while holding the rest fixed.
Example: Remove candle features to test their contribution under the same costs and risk limits.
Adverse selection
A tendency to trade when the counterparty’s information or timing makes the fill unfavorable.
Example: A passive buy can fill just before the market moves lower.
Antiderivative
A function whose derivative equals the given function.
Example: x² is an antiderivative of 2x; adding a constant gives another.
ATR
Average true range: a smoothed measure of bar range including gaps from the prior close.
Example: Divide a price distance by prior ATR to express it in comparable range units.
Autocorrelation
Correlation of a series with a lagged version of itself.
Example: Lag-one autocorrelation compares observations one step apart.
Availability timestamp
The time at which a value could first have been used by the modeled decision process.
Example: A report about the previous quarter becomes usable after its release and processing delay.
Backpressure
A mechanism that limits incoming work when a consumer cannot keep up.
Example: A bounded event queue forces a defined overload policy.
Backtest
A historical simulation of a fully specified decision and execution process.
Example: A signal at today’s close must use a subsequently eligible execution price.
Baseline
A simple, predeclared comparator for evaluating incremental value.
Example: Compare a neural forecast with a trailing mean on the same periods.
Basis point
One hundredth of a percentage point; 0.0001 as a decimal.
Example: 10 basis points is 0.1%, or 0.001.
Bayesian updating
Combining a prior belief with the likelihood of observed evidence.
Example: Evidence that is more likely under one hypothesis shifts its posterior weight upward.
Bellman equation
A recursive relation connecting value now to immediate reward and future value.
Example: The continuation value must use the next-state distribution and chosen policy or optimization.
Bootstrap
A resampling procedure used to estimate uncertainty under a chosen dependence model.
Example: Block resampling preserves some local time dependence; it does not create an untouched test set.
BOS
Break of structure: a specified break in the established swing direction.
Example: In the stated up-state convention, a close above the confirmed high is bullish BOS.
Breakout
A specified observation beyond a boundary fixed before the observation.
Example: A close above a prior high plus a one-unit buffer is a reproducible trigger.
Broadcasting
Rules that align array dimensions for elementwise operations without explicit repetition.
Example: A column vector times a row vector forms a matrix, which can be an accidental shape bug.
Brownian motion
A continuous-time process with independent Gaussian increments and variance proportional to elapsed time.
Example: A time increment .04 has Brownian standard deviation .2.
Calibration
Agreement between predicted probabilities and observed frequencies across comparable cases.
Example: Among many events assigned probability .7, roughly 70% should occur if predictions are well calibrated.
Candlestick
A display of a bar’s open, high, low and close.
Example: The body joins open and close; wicks extend to the extremes.
Capacity
The scale at which a strategy remains viable under liquidity, impact and operating constraints.
Example: An edge on a small order may disappear when participation increases.
Cash flow
An amount paid or received at a specified time.
Example: An investor deposit increases cash but is not trading profit.
Chain rule
Multiply the sensitivities along a composition of functions.
Example: For y=(2x+1)², the derivative is 4(2x+1).
CHOCH
Change of character: a specified break against the established structure.
Example: In the stated up-state convention, a close below the protected low is bearish CHOCH.
CNN
A convolutional neural network that applies shared filters across positions.
Example: A one-dimensional CNN can process a sequence of candle features.
Cointegration
A stationary linear combination of individually nonstationary series under a specified model.
Example: High correlation alone does not establish cointegration.
Conditional probability
An event probability given specified information.
Example: The chance of a loss conditional on a volatility regime may differ from the unconditional chance.
Confidence interval
An interval from a procedure with a stated repeated-sampling coverage under its assumptions.
Example: A 95% procedure aims to cover the fixed parameter in 95% of repeated samples.
Constant rate
A change per unit time that remains fixed over the modeled interval.
Example: Adding 2 units each hour to an initial 5 gives 11 units after 3 hours.
Constraint
A condition limiting allowed choices.
Example: Portfolio weights may be required to sum to one.
Continuity
Agreement between a function’s value and its limit at a point.
Example: A removable hole can have a limit without a defined function value.
Contrastive learning
Learning representations by drawing selected examples together and separating others.
Example: The choice of positive and negative pairs determines what similarity means.
Correlation
A standardized measure of linear co-movement.
Example: Assets can be highly correlated without forming a stationary tradable spread.
Covariance
Expected joint movement of two variables relative to their means.
Example: Two returns moving together contribute positive covariance under the model.
Cross-validation
Repeated separation of fitting and evaluation samples under a defined sampling scheme.
Example: Trading labels require chronological and overlap-aware splits.
Curvature
How a curve bends; the second derivative describes changes in slope.
Example: For x², the second derivative is 2 everywhere.
Data leakage
Information crossing a boundary that should separate fitting, selection or evaluation.
Example: Scaling all observations before splitting lets test data influence training.
Day-count convention
A rule for converting dates into accrual fractions for a financial contract.
Example: Actual/360 and Actual/365 can produce different interest accruals.
Delta
A derivative price’s local sensitivity to its underlying price, holding other inputs fixed.
Example: Delta .6 approximates a .60 price change for a small one-unit underlying move.
Denominator
The expression below a fraction bar; it cannot be zero in ordinary division.
Example: In three quarters, 4 specifies the number of equal parts.
Dependency lockfile
A record of resolved software versions used to reproduce an environment.
Example: A library update should trigger numerical regression checks before adoption.
Derivative
The local rate of output change with respect to an input, when the limit exists.
Example: For f(x)=x² at x=3, the derivative is 6 output units per input unit.
Derivative contract
A contract whose cash flows depend on a specified underlying asset, rate or event.
Example: An option and a futures contract can reference the same underlying but create different obligations.
Differential equation
An equation relating a function to its derivatives.
Example: A constant growth rate and a starting balance determine a linear path.
Diffusion
A continuous-time stochastic model driven by a Brownian component.
Example: Drift controls modeled local average change; diffusion scale controls local uncertainty.
Discounting
Converting future cash flows into present values with a specified rate model.
Example: At 10% for one period, 110 due later has present value 100.
Distribution
A model of possible outcomes and their probabilities.
Example: A fair die has six possible values with equal probability.
Divergence
A specified disagreement between confirmed price and indicator swings.
Example: A lower price low paired with a higher indicator low is one bullish convention.
Diversification
Combining exposures whose risks are not perfectly aligned.
Example: Ten highly similar strategies may provide little additional diversification.
Domain
The inputs for which an expression is defined.
Example: The real-valued function log(x) requires x>0.
Dot product
The sum of pairwise products of corresponding vector entries.
Example: [2,3] dotted with [4,5] gives 23.
Drawdown
Decline from a previous peak in the chosen wealth series.
Example: Falling from 100 to 80 is a 20% drawdown.
Drift
The modeled instantaneous conditional mean rate of change.
Example: A positive drift does not ensure every realized price increment is positive.
DTW
Dynamic time warping: an alignment minimizing accumulated local mismatch subject to allowed moves.
Example: A band limits how far observation positions can shift during matching.
Duration
A local measure of bond-price sensitivity to yield, under a stated convention.
Example: Modified duration 5 implies about a 5% price decline for a one-percentage-point yield rise, locally.
Eigenvalue
A scaling factor for a direction preserved by a matrix transformation.
Example: An eigenvector changes length, but not its direction, under that transformation.
Elliott Wave
A framework for classifying price swings into specified impulse and corrective patterns.
Example: A finished five-wave count cannot be assumed known during the third wave.
Embargo
Excluding a specified interval near an evaluation boundary to limit information overlap.
Example: A gap of several observations is justified by the actual information timeline, not by convention alone.
Embedding
A learned numerical representation of an input.
Example: Nearby coordinates indicate similarity under the learning objective, not guaranteed similar returns.
Equation
A statement that two expressions have equal values.
Example: 2x+1=7 gives x=3.
Euler method
A numerical update using the current rate over a finite time step.
Example: Starting at 5 with rate 2 per hour, a half-hour Euler step reaches 6.
Event-driven backtest
A simulation that updates state in an explicit sequence of market, order and fill events.
Example: A signal submits an order; a later fill changes cash and inventory.
EWMA
An exponentially weighted moving average giving declining weight to older observations.
Example: A larger new-observation weight reacts faster and smooths less.
Excess return
Return less a stated reference return over the same interval.
Example: A 1% portfolio return minus a 0.2% benchmark return gives 0.8 percentage points.
Expected shortfall
Average loss in a specified worst-probability tail, with a stated convention for boundary mass.
Example: A 95% measure concerns the worst 5% of losses under the model.
Expected value
The probability-weighted average of possible outcomes.
Example: An equal chance of +10 or −4 gives expected payoff 3 before costs.
Exponential
A function whose variable appears in an exponent.
Example: exp(0)=1; multiplying exp(a) by exp(b) gives exp(a+b).
Feature
An input supplied to a statistical or machine-learning model.
Example: A completed candle’s signed body fraction is one numerical feature.
Feature pipeline
A reproducible sequence of transformations from raw observations to model inputs.
Example: Fit missing-value handling and scaling only on the training window.
Function
A rule assigning one output to each allowed input.
Example: For f(x)=x², input 3 produces output 9.
Funding rate
A periodic transfer rate under a perpetual-derivative contract’s venue rules.
Example: Funding cash flow depends on side, notional, rate and settlement time.
Futures
Contracts creating specified settlement obligations on a stated underlying and expiry.
Example: The quoted price change must be multiplied by the contract multiplier and quantity.
FVG
Fair value gap: here, a three-bar non-overlap convention between the first and third bar.
Example: First high 102 and third low 104 define a bullish zone [102,104].
Gamma
The sensitivity of delta to the underlying price.
Example: Gamma describes how the local hedge ratio changes as spot moves.
Gann angle
A chart line defined by specified price and time units.
Example: A 1×1 line is one chosen price unit per time unit; its screen angle changes with scaling.
GARCH
A model updating conditional variance from earlier shocks and variance.
Example: A large squared residual can raise the next variance forecast.
GASF
Gramian angular summation field: a matrix encoding pairwise angular relationships of scaled values.
Example: It rearranges information from a sequence; it does not add new market observations.
Gradient
The vector of first partial derivatives.
Example: For f(x,y)=x+2y, the gradient is [1,2].
Gradient descent
An iterative update moving parameters opposite an estimated objective gradient.
Example: The learning rate controls the step size; a large step can overshoot.
Gross exposure
Sum of absolute position notionals divided by capital under a stated valuation convention.
Example: A 60% long and 40% short book has 100% gross exposure.
Harmonic pattern
An ordered pivot sequence constrained by specified leg ratios and tolerances.
Example: One matching AB-to-XA ratio does not complete a Gartley detector.
Hedge ratio
The relative quantities chosen to offset a specified exposure.
Example: A regression coefficient needs conversion into quantities and contract units.
Heikin-Ashi
An OHLC transformation that uses price averages and a recursive opening value.
Example: Its synthetic close need not be an executable market price.
Hessian
The matrix of second partial derivatives.
Example: It describes local curvature in several directions, rather than just the slope.
Heteroskedasticity
Variation in conditional error variance across observations or time.
Example: Return uncertainty can rise sharply during a volatility episode.
Hidden state
An unobserved model state inferred from observations.
Example: A hidden regime may be inferred from observed returns rather than directly recorded.
Hyperparameter
A choice controlling a model or training procedure rather than an ordinary fitted coefficient.
Example: Tree depth and learning rate are hyperparameters.
Idempotency
A property that repeating the same operation has the same effect as performing it once.
Example: Replaying a fill identifier should not add the quantity twice.
Implementation shortfall
Difference between an actual execution outcome and a stated decision-price benchmark, including the chosen cost components.
Example: Delay, fills and unexecuted quantity can each contribute.
Information ratio
Mean active return divided by its standard deviation under a stated frequency and annualization convention.
Example: Use active returns against the same benchmark, not total portfolio volatility.
Initial condition
The value that specifies where a dynamic model starts.
Example: y(0)=5 fixes the starting amount at time zero.
Integral
An accumulation of contributions over an interval or region.
Example: A flow of 3 litres per minute for 4 minutes adds 12 litres.
Integration by parts
An integration identity derived from the product rule.
Example: Choose one factor to differentiate and another to integrate, then check the boundary term.
Itô correction
The extra second-order term caused by Brownian quadratic variation.
Example: An ordinary chain rule omits this term when transforming a diffusion.
Jacobian
The matrix of first derivatives of several outputs with respect to several inputs.
Example: Each row tracks how one output responds to the input coordinates.
Kelly
Position sizing that maximizes expected logarithmic wealth under a specified return model.
Example: Estimation error can make a model’s full Kelly allocation excessively aggressive.
Kill switch
A controlled mechanism for stopping new activity and handling outstanding risk according to policy.
Example: Stopping order submission alone does not cancel resting orders.
Lag
A previous observation measured in the series’ time steps.
Example: At daily bar 10, lag one is bar 9.
Latency
Elapsed time between specified events in a data or execution process.
Example: Measure decision-to-acknowledgment separately from decision-to-fill latency.
Leverage
Exposure relative to the capital supporting it, under a stated definition.
Example: Exposure 300 against equity 100 is three times equity.
Limit
The value approached as the input approaches a point.
Example: As x approaches 2, x+2 approaches 4.
Liquidity
The ability to trade a quantity promptly at a stated cost.
Example: A narrow spread for one share does not imply deep liquidity for a large order.
Log return
The natural logarithm of the ratio of ending to starting positive wealth.
Example: A wealth ratio of 1.02 gives log(1.02), approximately 0.019803.
Logarithm
The exponent needed to produce a positive value from a specified base.
Example: Because 2³=8, the base-two logarithm of 8 is 3.
Look-ahead bias
Using information before it was actually available at the simulated decision time.
Example: Fitting a scaler on the complete dataset leaks future information.
Loss function
The objective measuring model error or a training preference.
Example: Squared prediction error penalizes larger misses more heavily.
Margin
Collateral required under a trading or contract arrangement, not a general measure of maximum loss.
Example: Futures initial margin supports an exposure that can be much larger than the collateral.
Market impact
A trade’s effect on available prices and subsequent execution costs.
Example: A larger order may consume several levels of quoted liquidity.
Markov
A model where the specified current state contains the information needed for the next-state distribution.
Example: A two-state regime model uses transition probabilities out of the current state.
Matrix
A rectangular array representing relationships or transformations.
Example: A two-asset covariance matrix has two rows and two columns.
Mean
The sum of values divided by their count.
Example: The mean of 2, 5 and 8 is 5.
Mean reversion
A modeled tendency for a deviation to move toward a reference level.
Example: Reversion speed and the stability of the reference are separate assumptions.
Model drift
A change in the relationship between model inputs and outcomes or in their distributions.
Example: A model calibrated in one liquidity regime can deteriorate in another.
Momentum
Past directional movement or relative strength measured over a specified lookback.
Example: A trailing return is an input hypothesis, not a future return.
Monte Carlo
Numerical estimation by simulating draws from a specified model.
Example: Average many simulated payoffs to estimate the model’s expected payoff.
Multiple testing
Evaluating many hypotheses or variants, increasing opportunities for apparently favorable chance results.
Example: The best of 1,000 noisy strategies needs a selection-aware evaluation.
Net exposure
Signed sum of position notionals divided by capital under a stated valuation convention.
Example: A 60% long and 40% short book has 20% net exposure.
Notional
A reference measure of the economic exposure controlled by a position.
Example: Contract count × multiplier × reference price is one common futures convention.
Numerator
The expression above a fraction bar.
Example: In three quarters, 3 counts the selected parts.
OHLCV
Open, high, low, close and volume recorded for a bar.
Example: A daily bar does not reveal the exact sequence of all intraday trades.
Optimization
Choosing a feasible input to minimize or maximize a stated objective.
Example: Minimize modeled risk subject to position limits; the result depends on the model.
Option
A contract granting a specified exercise right under agreed terms.
Example: A call grants a right to buy at its strike; its premium is not its notional exposure.
Order book
A venue-specific collection of resting orders or aggregated price levels.
Example: Best bid and ask show only part of the liquidity available across venues.
Oscillator
An indicator describing recent movement on a chosen scale, often bounded.
Example: Stochastic %K measures a close’s position inside a recent range.
Out-of-sample
Data withheld from the relevant fitting and selection procedure.
Example: Repeatedly tuning to a test set makes it part of model selection.
Overfitting
Adapting a model or rule to sample-specific noise that does not generalize.
Example: Selecting the best of thousands of noisy backtests can produce an apparent winner.
Paper trading
Simulated order operation using a mock or broker-provided paper environment.
Example: A paper fill can be easier to obtain than a real fill at the same quote.
Partial derivative
Sensitivity to one independent input while holding the others fixed.
Example: For f(x,y)=x+2y, changing x by 1 with y fixed changes f by 1.
Partial fill
Execution of only part of an order quantity.
Example: An order for 100 shares can receive fills of 30 and 20 while 50 remain.
PDE
A partial differential equation involving derivatives in several independent variables.
Example: An option-pricing model may involve both time and underlying price.
Pivot
A turning-point candidate under a specified detection and confirmation rule.
Example: A pivot needing two later bars becomes available two bars after the extremum.
Point-in-time data
Data reconstructed according to what was actually available at a historical decision time.
Example: A revised earnings value must not replace the original value in an earlier backtest.
Policy
A rule or distribution for choosing an action from the available state.
Example: A policy may choose how much inventory to trade at the next decision time.
Portfolio
A collection of positions considered jointly.
Example: Two positions need a joint risk assessment, not just separate volatility estimates.
Power
Repeated multiplication for a positive integer exponent; other exponents require their domain conventions.
Example: 2³ means 2×2×2=8.
Power rule
Differentiate a power by multiplying by its exponent and reducing the exponent by one, on its differentiable domain.
Example: The derivative of x³ is 3x².
Probability
A number from zero to one assigned to an event under a specified model.
Example: A fair die assigns probability one sixth to any one face.
Property-based test
A test that checks general invariants over many generated inputs.
Example: Doubling fixed quantities should double a linear cash-flow calculation.
Purging
Removing training observations whose label-information intervals overlap a held-out evaluation period.
Example: A five-day target may cross a split even when its feature row precedes it.
Quantile
A cutoff at a specified cumulative probability.
Example: A loss quantile is not a cap on losses beyond that cutoff.
Random seed
An initialization value for a pseudorandom generator.
Example: A fixed seed repeats a simulation but does not establish that its assumptions are correct.
Rate limit
A service constraint on request frequency or volume over a specified interval.
Example: Retrying too quickly after throttling can worsen a data outage.
Ratio
One quantity divided by another; the units determine its meaning.
Example: 6 dollars shared across 3 items gives 2 dollars per item.
Reconciliation
Checking that independent records explain the same balances and changes.
Example: Starting equity plus investment profit plus external flows should match ending equity.
Regression
A model relating an outcome to one or more explanatory inputs.
Example: A linear regression estimates a slope and intercept; it does not establish causation.
Regularization
A penalty or restriction that discourages overly flexible fitted models.
Example: Ridge regression shrinks coefficients toward zero using a chosen penalty.
Reinforcement learning
Learning a policy from sequential actions and rewards in an environment.
Example: Execution research can model remaining inventory as part of the state.
Renko
A price-movement chart constructed from bricks under a chosen size and reversal convention.
Example: Multiple bricks may be emitted by one source-price jump at one timestamp.
Reproducibility
Ability to reconstruct a result from recorded inputs, code, configuration and environment.
Example: Save data hashes, versions, split boundaries and random seeds with a run.
Residual
Observed value minus the model’s prediction.
Example: An observation of 12 and forecast of 10 give residual 2.
Resistance
A candidate price area where an advance may meet a reaction.
Example: A level can fail or change its role after a confirmed break.
Retracement
The portion of a completed move subsequently given back.
Example: A move from 100 to 120 followed by 110 retraces half the upswing.
Reward
The immediate outcome signal specified for an RL agent.
Example: A reward can include marked profit minus trading costs and an inventory penalty.
Riemann sum
An approximation to accumulated area using rectangles.
Example: Four rectangles of width .5 sample a curve over an interval of length 2.
Risk contribution
An allocation of portfolio risk to holdings under a specified decomposition.
Example: A small capital weight can dominate risk when its volatility and correlations are large.
Sample
The observations available for analysis.
Example: Twenty recorded trades are a sample, not every possible future trade.
Secant
A line through two points on a curve.
Example: For x² between x=2 and x=3, the slope is 5.
Shapelet
A short sequence used as a candidate local pattern or matching feature.
Example: Compare a fixed training template with windows in the available history.
Sharpe ratio
Mean excess return divided by its standard deviation using consistent horizons.
Example: Annualization requires additional assumptions about return dependence.
Simple return
Price change plus distributions, divided by initial price, for a specified holding interval.
Example: Buying at 100 and selling at 103 without distributions gives a 3% holding-period return.
Slippage
The difference between a chosen reference price and actual execution price.
Example: Paying 100.03 against a buy reference of 100 adds .03 per unit.
Slope
Output change per unit of input change.
Example: A rise of 6 over an input change of 2 gives slope 3.
Spread
A difference between two prices or rates, whose meaning depends on context.
Example: Bid–ask spread measures quoted transaction friction; a pair spread compares two assets.
Square root
The nonnegative number whose square equals the given nonnegative value.
Example: The square root of 9 is 3; solving x²=9 separately allows both 3 and −3.
Standard deviation
The square root of variance, expressed in the original measurement units.
Example: Variance 9 dollars squared corresponds to standard deviation 3 dollars.
Standard error
Estimated variability of an estimator across repeated samples.
Example: For independent observations, a mean’s standard error typically shrinks with the square root of sample size.
Stationarity
Stability of specified distributional properties over time.
Example: Weak stationarity requires a constant mean and lag-dependent covariance, not constant prices.
Substitution
A change of variable that rewrites a calculation in simpler terms.
Example: Set u=2x+1 and account for du=2 dx in an integral.
Support
A candidate price area where a decline may meet a reaction.
Example: A support touch is an observation; it does not guarantee a bounce.
Survivorship bias
Distortion from selecting only entities that remain in the dataset at the end.
Example: Backtesting current index members excludes some companies that failed or were removed.
Tangent
A line matching a differentiable curve’s local slope at a point.
Example: The tangent to x² at x=3 has slope 6.
Target
The outcome a model is trained to predict, with a defined availability time.
Example: A five-day forward return is known only after those five days have elapsed.
Taylor approximation
A local polynomial built from a function’s value and derivatives.
Example: Near zero, exp(x) is approximately 1+x; accuracy depends on the distance and omitted terms.
Tick
The smallest permitted quoted price increment for a stated instrument.
Example: A .25-point tick with a 50-per-point multiplier changes contract value by 12.50.
Tracking error
Standard deviation of portfolio returns minus benchmark returns at a specified horizon.
Example: Two portfolios with equal volatility can have very different tracking errors.
Transformer
A neural architecture using attention to combine information across input positions.
Example: A causal attention mask prevents attending to later tokens in the current sequence.
Unit test
A small automated check of a component against an independently specified expectation.
Example: A hand-calculated fee fixture checks the sign and unit conversion.
Variable
A named quantity whose value may change.
Example: In y=2x+1, changing x changes y.
Variance
Average squared deviation from the mean; the sample estimator commonly uses n−1.
Example: Squaring deviations prevents positive and negative deviations from canceling.
Vector
An ordered list of quantities.
Example: [.25,.75] can represent weights in two assets.
Vectorization
Expressing operations on arrays so numerical kernels process many elements together.
Example: Multiply a vector of held exposures by a matching vector of returns.
Volatility
The scale of return or price fluctuations under a stated horizon and measure.
Example: Daily and annual volatility use different time conventions.
Volume
Quantity traded under a specified instrument and venue convention.
Example: Total volume includes both sides of every executed trade.