Agent-Based Model (ABM)
A computational simulation in which autonomous agents interact according to simple rules, producing emergent market-level phenomena.
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Complex Systems Terminology
A reference of complex systems, prop trading, options strategy, and finance concepts that shape how we build tools.
AI Agent-Based Model (AABM)
A computational simulation in which autonomous agents learn and adapt via artificial intelligence instead of fixed rules, producing emergent market-level phenomena.
Attractor / Basin of Attraction
A stable state or dynamic pattern toward which a system tends to evolve; the basin is the set of initial conditions that converge there.
Counterfactual
A hypothetical outcome differing from what actually occurred, used to test strategies against alternate market histories.
Criticality / Self-Organized Criticality
The tendency of a system to arrange itself near a tipping point, where small events can trigger disproportionately large cascades.
Emergence
Macroscopic patterns or behaviors that arise from local interactions among many individuals, without central coordination.
Fat Tails
A probability distribution with higher-than-normal likelihood of extreme outcomes; common in financial returns.
Feedback Loops
Channels where an action reinforces (positive) or dampens (negative) itself, driving amplification or stabilization.
Granovetter Threshold Models
Collective-action models in which each individual acts once the share of others acting crosses their personal threshold, producing cascades and tipping points.
Heterogeneous Agents
Agents in a model that differ in rules, beliefs, time horizons, or constraints, producing more realistic behavior than representative-agent models.
Herding
The tendency of traders to mimic each other’s behavior, producing correlated demand shocks and bubble-like dynamics.
Information Cascades
A sequential process where individuals override private information to follow observed actions, amplifying mispricing.
Micro-Macro Problem
The classic sociological question of how system-level outcomes arise from individual actions and interactions; emergent patterns cannot be derived by simply aggregating individuals.
Multiverse Backtesting
Running strategies across many alternate simulated histories to assess robustness beyond the single realized market path.
Network Effects
Changes in behavior or value that arise from how agents are connected, such as contagion through counterparty networks.
Non-Ergodicity
A property where time averages and ensemble averages diverge; in trading, the path taken matters for survival.
Non-Walrasian
Describes markets that depart from Walrasian equilibrium assumptions. Instead of a frictionless auctioneer clearing prices instantly, heterogeneous agents with incomplete information trade through decentralized interactions.
Path Dependence
The idea that future outcomes depend on the sequence of past events, not just current conditions.
Power Law
A relationship where the frequency of an event varies as a power of its size, producing frequent small moves and rare large crashes.
Reflexivity
A two-way feedback loop between market prices and the expectations that influence them.
Structural Break
A point in time when the statistical properties of a market process change, rendering old models unreliable.
Alpha
Excess return generated by a strategy relative to a benchmark or risk model.
Algorithmic Trading
The use of automated rules and execution logic to enter, manage, and exit trades with minimal human intervention.
Backtesting
Evaluating a strategy on historical data to estimate performance, risks, and drawdown characteristics.
Beta
A measure of an asset’s sensitivity to broad market movements; beta of 1 moves with the market.
Carry Trade
A strategy that borrows in a low-yielding asset and invests in a higher-yielding one, profiting from the spread.
High-Frequency Trading (HFT)
A subset of algorithmic trading characterized by extremely short holding periods and high turnover.
Mean Reversion
The hypothesis that prices and spreads tend to return toward a long-run average after deviations.
Momentum
A strategy that buys assets with rising prices and sells those with falling prices, betting on trend continuation.
Overfitting
When a strategy is tuned too closely to historical noise, producing excellent backtests but poor live performance.
Pairs Trading
A market-neutral strategy that trades the relative spread between two historically correlated assets.
Prop Trading
Trading financial instruments with a firm’s own capital rather than client funds, seeking direct profit.
Slippage
The difference between expected execution price and actual fill price, often due to liquidity or latency.
Statistical Arbitrage
A family of strategies that exploit short-term statistical mispricings across many instruments.
Trend Following
A systematic approach that enters positions in the direction of established price trends and exits when they reverse.
Walk-Forward Analysis
A backtesting procedure that periodically re-trains and validates a strategy on rolling out-of-sample windows.
Butterfly Spread
An options strategy combining bull and bear spreads to create a limited-risk position with peak profit at a target strike.
Calendar Spread
A strategy that buys and sells the same strike option in different expiration months to exploit term-structure differences.
Call Option
A contract giving the buyer the right, but not the obligation, to buy an asset at a set strike price before expiration.
Convexity
The non-linear payoff profile of an option, where gains can accelerate and losses decelerate relative to the underlying.
Delta
The sensitivity of an option’s price to a one-unit change in the underlying asset’s price.
Gamma
The rate of change in delta as the underlying price moves; a measure of convexity exposure.
Implied Volatility (IV)
The market’s forecast of future volatility embedded in an option’s current price.
Iron Condor
A non-directional options strategy that profits when the underlying stays within a defined range through expiration.
Put Option
A contract giving the buyer the right, but not the obligation, to sell an asset at a set strike price before expiration.
Straddle
Buying both a call and put at the same strike and expiration, profiting from large moves in either direction.
Strangle
Buying out-of-the-money call and put options, a cheaper way to bet on volatility than a straddle.
Theta
The daily decay in an option’s value due to the passage of time, all else equal.
Vega
The sensitivity of an option’s price to changes in implied volatility.
Vertical Spread
An options strategy that buys and sells options of the same type and expiration but different strikes to limit risk.
Volatility Skew / Smile
The pattern where implied volatility varies across strike prices, often higher for downside strikes.
Closed-Form Solution
An analytical solution expressed as a finite mathematical formula evaluated directly, in contrast to numerical approximation or simulation-based methods.
Copula
A function that joins marginal distributions into a joint distribution, capturing dependence structure separately from individual volatilities; used to model how assets move together under stress.
Drawdown
The peak-to-trough decline in portfolio value, used to measure strategy pain and recovery.
Endogeneity
When variables are determined within the system being modeled rather than imposed externally; in econometrics, correlation between an explanatory variable and the error term that biases causal inference.
Expected Shortfall (CVaR)
The average loss in the worst-tail scenarios beyond a chosen confidence level, a coherent risk measure.
Filtered Historical Simulation
A scenario-generation method that filters historical return shocks through a fitted volatility process, producing realistic fat-tailed loss distributions without assuming a parametric distribution.
Kelly Criterion
A formula for determining the optimal bet size to maximize long-run wealth growth given edge and odds.
Kurtosis
A statistic describing the thickness of distribution tails; high kurtosis indicates fat-tail risk.
Market Regime
A persistent market environment characterized by specific volatility, correlation, and trend dynamics.
Maximum Adverse Excursion (MAE)
The largest loss experienced by a trade while it is open, useful for diagnosing position-management flaws.
Regime-Specific Sizing
Adjusting position size based on the current market regime rather than applying a static allocation rule.
Regime Switching
A class of statistical models in which a market process transitions between distinct regimes, such as high- and low-volatility states, with transition probabilities estimated from data.
Robustness
A strategy’s ability to perform acceptably across a wide range of market conditions and parameter values.
Sharpe Ratio
Risk-adjusted return calculated as excess return divided by volatility.
Skewness
A measure of distribution asymmetry; negative skew indicates a higher probability of large downside moves.
Sortino Ratio
A Sharpe-like measure that uses only downside deviation rather than total volatility.
Value at Risk (VaR)
A statistical estimate of the maximum expected loss over a defined period at a given confidence level.
Volatility Clustering
The tendency of large price moves to be followed by further large moves, and calm periods to follow calm periods.
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