Quant Interview Glossary

The unconditional prevalence of an event before any specific evidence is taken into account.

A rule for updating the probability of a hypothesis when new evidence arrives.

A single experiment with exactly two outcomes, conventionally labelled success and failure.

The number of successes in a fixed number of independent trials with constant success probability.

The continuous-time limit of a random walk, with independent normally distributed increments.

The mean of many independent finite-variance samples is approximately normally distributed.

The number of ways to choose k items from n when order does not matter.

The expected value of a random variable given the value of another - itself a random variable.

The probability of an event given that another event is known to have occurred.

The probability that a random variable takes a value at or below a given point.

The probability-weighted average of all possible outcomes of a random variable.

The continuous waiting time until the next event in a process with a constant arrival rate.

The problem of a random walk between zero and a target, and the probability of hitting each first.

The number of trials up to and including the first success in repeated independent attempts.

A method for counting a union of overlapping sets by alternately adding and subtracting intersections.

Two events are independent when knowing one occurred does not change the probability of the other.

A variable equal to 1 when an event occurs and 0 otherwise, whose expectation is the event's probability.

The bet size that maximises the long-run growth rate of a bankroll.

The sample average converges to the true mean as the number of independent observations grows.

The probability of an event is the sum of its probabilities across a partition of the sample space.

Expectations of a sum equal the sum of expectations, even when the variables are dependent.

A distribution whose logarithm is normally distributed, used to model asset prices.

A process where the next state depends only on the current state, not on the path taken to reach it.

A process whose expected next value, given everything so far, equals its current value.

The property that the time already waited gives no information about the remaining wait.

Two events that cannot both occur, so their intersection has probability zero.

The symmetric bell-shaped distribution that arises from summing many independent contributions.

The values of a sample arranged in sorted order, such as the minimum, maximum or median.

The number of ordered arrangements of items.

The count of events in a fixed interval when they occur independently at a constant average rate.

The probability assigned to a hypothesis before observing the current evidence.

A function whose integral over an interval gives the probability a continuous variable falls in it.

A function mapping outcomes of a random experiment to numbers.

A process that moves by independent random steps, whose typical distance grows with the square root of time.

The probability that a bankroll hits zero before reaching a target, given a betting strategy.

The square root of variance, expressing dispersion in the same units as the data.

The long-run distribution over states that a Markov chain settles into and then preserves.

A distribution where every value in an interval is equally likely.

A function mapping wealth to satisfaction, used to explain why people do not maximise expected value.

The expected squared deviation from the mean, measuring how spread out a distribution is.

Correlation of a series with its own lagged values.

A simulation of how a strategy would have performed on historical data.

The decomposition of prediction error into systematic error, sensitivity to the sample, and irreducible noise.

Estimating the sampling distribution of a statistic by resampling the observed data with replacement.

A range constructed so that, across repeated samples, a stated proportion of such intervals contain the true value.

Covariance normalised by both standard deviations, giving a unit-free measure between -1 and 1.

A measure of how two variables move together, in the product of their units.

The matrix of pairwise covariances between a set of variables, central to portfolio risk.

Estimating out-of-sample performance by repeatedly training on part of the data and testing on the rest.

The average loss in the worst outcomes beyond the value-at-risk threshold.

A distribution with more probability of extreme outcomes than a normal distribution.

Non-constant error variance across observations, violating a standard regression assumption.

A procedure for deciding whether data is inconsistent with a stated null hypothesis.

A measure of tail heaviness, with the normal distribution as the reference point at 3.

Fitting a linear relationship by minimising the sum of squared residuals.

Using information in a backtest that would not have been available at the time of the decision.

Choosing the parameter values that make the observed data most probable.

High correlation among predictors, which makes individual regression coefficients unstable.

The inflation of false positives that occurs when many hypotheses are tested on the same data.

Fitting noise rather than signal, producing excellent in-sample performance and poor out-of-sample results.

The probability of observing data at least as extreme as yours, assuming the null hypothesis is true.

The proportion of variance in the dependent variable explained by the model.

Penalising model complexity to reduce variance at the cost of some bias.

Excess return divided by volatility, measuring return per unit of risk.

A measure of distributional asymmetry around the mean.

The standard deviation of an estimator, quantifying how much an estimate would vary across samples.

The property that a series' statistical characteristics do not change over time.

Distortion caused by analysing only entities that survived, excluding those that failed.

An estimator whose expected value equals the true parameter.

The loss threshold that will not be exceeded with a given probability over a given horizon.

The tendency of large price moves to be followed by large moves, and calm periods by calm periods.

A closed-form model for European option prices under continuous hedging and constant volatility.

A contract giving the right, but not the obligation, to buy an asset at a fixed strike price.

Descriptions of whether forward prices sit above or below the current spot price.

Curvature in the relationship between an instrument's value and an underlying variable.

The net cost of holding an asset until a future date, which determines the forward price.

The rate of change of an option's value with respect to the underlying price.

Offsetting an option's directional exposure by holding delta units of the underlying.

An agreement to buy or sell an asset at a fixed price on a future date.

An exchange-traded forward that is margined and settled daily.

The rate of change of delta with respect to the underlying price - the curvature of the option payoff.

Profiting from a long-gamma position by rehedging, which mechanically buys low and sells high.

The standard model for asset prices, in which log returns follow Brownian motion with drift.

The volatility input that makes a pricing model reproduce an option's market price.

The value an option would have if exercised immediately, never below zero.

The chain rule for functions of stochastic processes, with an extra second-order term.

How far an option's strike sits from the current price of the underlying.

A contract giving the right, but not the obligation, to sell an asset at a fixed strike price.

A no-arbitrage relationship linking the prices of a European call, put, the underlying and cash.

The volatility actually observed in an asset's price over a past period.

Constructing a portfolio of simpler instruments that reproduces a derivative's payoff in every state.

The sensitivity of an option's value to a change in interest rates.

Valuing a derivative as the discounted expected payoff under a probability measure where all assets drift at the risk-free rate.

A long call and long put at the same strike and expiry - a direction-neutral bet on movement.

The fixed price at which an option holder may buy or sell the underlying asset.

A combination of instruments that replicates the payoff of a different single instrument.

The rate at which an option loses value as time passes, holding everything else constant.

The sensitivity of an option's value to a one-point change in implied volatility.

Buying one option and selling another of the same type at a different strike.

The standard deviation of returns, expressing how much an asset's price fluctuates.

The gap between arithmetic and geometric average returns caused by compounding volatility.

The pattern of implied volatility varying across strikes, contradicting the constant-volatility assumption.

The tendency to trade precisely with counterparties who know something you do not.

A trade that produces a risk-free profit with no net capital at risk.

The residual risk from hedging with an instrument that does not exactly match the exposure.

The sensitivity of an asset's returns to the returns of a benchmark.

The difference between the highest price buyers will pay and the lowest sellers will accept.

The return earned from holding a position when nothing changes.

The expected profit per trade, in the units of the trade.

The proposition that asset prices already reflect available information.

Taking an offsetting position to reduce exposure to a particular risk.

Order flow from counterparties trading on information the market maker does not have.

The price risk a market maker carries while holding a position acquired from providing liquidity.

The delay between an event occurring and a system responding to it.

An order to trade at a specified price or better, which rests in the book until filled or cancelled.

The ability to trade size quickly without moving the price much.

Collateral posted to cover potential losses on a leveraged or derivative position.

The adverse price movement caused by executing an order.

A participant who quotes both a bid and an ask, profiting from the spread while managing inventory risk.

An order to trade immediately at the best available price.

The tendency of a series to return toward a long-run average after deviating from it.

The record of resting limit orders at each price level on both sides of a market.

A trade betting that the price relationship between two related instruments will revert.

Selling a borrowed asset with the intention of buying it back later at a lower price.

Shifting both sides of a market in one direction to encourage trades that reduce your position.

The difference between the expected execution price and the price actually achieved.

The minimum price increment at which an instrument may be quoted.

An execution strategy that spreads an order evenly over a time window.

The average price over a period weighted by volume traded at each price.

The tendency for the winner of a common-value auction to have overestimated the item's worth.

A description of how an algorithm's cost grows with input size, ignoring constants.

The degree to which a program accesses memory that is already in fast cache.

The factorisation of a positive definite matrix into a lower triangular matrix times its transpose.

A vector whose direction is unchanged by a linear transformation, and the factor by which it is scaled.

The binary representation of real numbers, which is approximate and has surprising failure modes.

A formal power series whose coefficients encode a sequence, turning combinatorial problems into algebra.

A sum where each term is a constant multiple of the previous one.

The sum of reciprocals of the integers, which diverges but only logarithmically.

A quantity unchanged by the allowed moves of a process, used to prove something is impossible.

For a convex function, the expected value of the function is at least the function of the expected value.

A method for optimising a function subject to equality constraints.

The rule for computing the expectation of a function of a random variable without deriving its distribution.

The inverse of exponentiation, converting products into sums.

Arithmetic where numbers wrap around after reaching a fixed modulus.

Estimating a quantity by averaging over many random simulations.

An iterative root-finding method using the derivative to converge quadratically.

Whether a quantity is odd or even, often preserved by a process and used as an invariant.

If more items are placed into fewer containers, at least one container holds more than one item.

A symmetric matrix for which x'Ax is positive for every non-zero vector x.

A rotation of the data into uncorrelated directions ordered by how much variance each explains.

The number of linearly independent rows or columns of a matrix.

Defining a quantity in terms of smaller instances of the same problem.

An expansion of a function as an infinite sum of its derivatives at a point.