Quant & Pricing
48 Quant & Pricing terms, defined in plain English — part of the 1345-term Finicade finance glossary. Each one has its own page, and links to the free game that teaches it.
- Automatic Differentiation
- Automatic differentiation computes exact derivatives of a program by applying the chain rule to its operations, rather than by bumping inputs and repricing.
- Backward Induction
- Pricing by starting at the payoff and working backwards step by step to today.
- Binomial Tree
- A pricing model that chops time into steps where the price can only go up or down, then works backwards from the payoff to today.
- Black–Scholes PDE
- The partial differential equation every option price must satisfy, derived by hedging away all the risk.
- Breeden-Litzenberger
- Breeden-Litzenberger extracts the market implied probability distribution from option prices: the second derivative of price by strike is the density.
- Brownian Motion
- The random, jittery path used to model how prices wander through time — borrowed from the physics of particles in a fluid.
- Change of Numéraire
- Choosing what to measure prices in — cash, a bond, a stock — to make a hard pricing problem simple.
- Cholesky Decomposition
- Cholesky decomposition factors a covariance matrix into a triangular matrix and its transpose — the step that turns independent draws into correlated ones.
- Closed-Form Solution
- A closed-form solution is an exact formula that returns a price directly, with no simulation or grid.
- Convexity Adjustment
- A convexity adjustment corrects for the fact that a non-linear payoff's expected value is not the value at the expected rate.
- Copula
- A mathematical tool for stitching individual distributions into a joint one, capturing how variables move together in the tails.
- Cox-Ingersoll-Ross Model
- The CIR model makes the short rate mean-reverting with volatility proportional to its square root, so the rate can approach zero but never go negative.
- Curve Bootstrapping
- Curve bootstrapping builds a zero-coupon curve step by step from traded instruments, using each shorter maturity's solved rate to strip the next.
- Day Count Convention
- A day count convention is the rule for turning a period between two dates into a fraction of a year — 30/360, actual/360, actual/365, actual/actual.
- Discount Factor
- The number you multiply a future cash flow by to get its value today — always less than one, and smaller the further out or the higher the rate.
- Feynman-Kac Theorem
- The Feynman-Kac theorem links PDEs to expectations of stochastic processes: a PDE solution equals the expected discounted payoff of a diffusion.
- Filtration
- A filtration is the formal record of what is known at each point in time — the mathematical object that stops a model from cheating with future information.
- Finite Difference Method
- The finite difference method prices derivatives by solving the pricing PDE numerically on a grid of price and time.
- Forward Rate
- A forward rate is the interest rate for a future period implied by today's curve — what you can lock in now to borrow between years two and three.
- Fundamental Theorem of Asset Pricing
- The result tying it all together: no arbitrage exists if and only if there's a risk-neutral probability measure that prices everything.
- Geometric Brownian Motion
- The standard model for a stock price: random Brownian shocks applied to percentage changes, so the price wanders but never goes negative.
- Girsanov's Theorem
- The mathematical licence to switch from the real world to the risk-neutral one by changing the drift of a random process.
- Heston Model
- The Heston model prices options with volatility that is itself random and mean-reverting, rather than the constant Black-Scholes assumes.
- Hull-White Model
- The Hull-White model extends Vasicek with a time-dependent drift chosen so the model reproduces today's observed yield curve exactly.
- Itô's Lemma
- The chain rule for random processes — how to find the change in a function of a wandering price.
- Jump Diffusion
- A pricing model that adds sudden jumps to the smooth wandering of Brownian motion — capturing crashes and gap moves that a pure diffusion misses.
- Least Squares Monte Carlo
- Least squares Monte Carlo prices early-exercise options by simulating paths forward, then regressing to estimate the continuation value at each step.
- Local Volatility
- A model where volatility isn't one number but varies with price and time, calibrated to match every option's market price at once.
- Markov Property
- The Markov property says the future depends only on the present state, not on the path that led there.
- Martingale
- A process whose best guess for tomorrow is exactly today's value — no drift, a mathematically 'fair game'.
- Model Calibration
- Calibration is choosing model parameters so the model reproduces prices actually observed in the market, rather than estimating them from history.
- Monte Carlo Simulation
- Pricing something by simulating thousands of random future paths and averaging the payoff.
- Nelson-Siegel Curve Fitting
- Nelson-Siegel fits a yield curve with a few parameters mapping to level, slope and curvature — the three factors behind almost all curve moves.
- No-Arbitrage
- The master assumption of pricing theory: you can't make a riskless profit from nothing, because any such gap would be traded away instantly.
- Poisson Process
- A Poisson process counts events that arrive randomly at a constant average rate, with waiting times that are exponentially distributed and memoryless.
- Random Walk
- A path where each step is random and independent of the last, so the best forecast of tomorrow is simply today.
- Replication
- Building a portfolio of simpler assets that exactly reproduces a derivative's payoff.
- Risk-Neutral Pricing
- Risk-neutral pricing values a derivative in a pretend world where every asset earns the risk-free rate — no-arbitrage makes that price right in reality.
- SABR Model
- SABR is the market-standard model for interest-rate smiles, with four parameters controlling level, backbone, volatility of volatility and correlation.
- Stochastic Differential Equation
- A stochastic differential equation describes how a quantity evolves with both a predictable drift and a random shock, written as dX = drift·dt + volatility·dW.
- Stochastic Process
- A quantity that evolves randomly through time — a stock price, an interest rate.
- Stochastic Volatility
- Modelling volatility as itself random and mean-reverting, rather than fixed.
- Structured Product
- A pre-packaged investment engineered from bonds and derivatives — for example, 'your money back plus half the market's upside'.
- Trinomial Tree
- A trinomial tree lets each node move up, down or sideways, giving an extra degree of freedom over a binomial tree.
- Variance Reduction
- Variance reduction is the set of tricks that make Monte Carlo converge with far fewer paths.
- Vasicek Model
- The Vasicek model describes the short interest rate as mean-reverting with constant volatility, the first tractable model of the whole yield curve.
- Volatility Surface
- The full map of implied volatility across every strike and maturity — the smile in one direction, the term structure in the other.
- Zero Rate
- A zero rate is the yield on a single cash flow at one maturity, with no coupons in between — the pure price of time for that date.