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Probability Distributions, Simulation, and Tail Risk

Probability distribution, heavy tails, Monte Carlo simulation, scenario analysis, and sensitivity analysis terms.

Probability Distributions, Simulation, and Tail Risk covers probability distribution, heavy tails, Monte Carlo simulation, scenario analysis, and sensitivity analysis terms.

Use these pages when a statistical assumption, model structure, or risk distribution changes the analytical result. It sits inside Valuation Modeling and Statistical Methods, so readers can move up when the broader valuation context matters.

Use the table below to choose the narrower valuation branch before relying on a model input, market multiple, forecast, risk premium, price signal, or recommendation.

What This Branch Covers

AreaUse it for
Heavy TailsHeavy tails describe probability distributions with more extreme outcomes than a normal distribution, affecting risk and loss modeling.
Monte Carlo SimulationMonte Carlo simulation estimates valuation or risk outcomes by running many randomized scenarios for uncertain inputs.
Probability DistributionA probability distribution describes possible outcomes and their likelihoods, forming the basis for risk, return, and scenario modeling.
Scenario AnalysisScenario analysis tests valuation, planning, or risk outcomes under coherent alternative sets of assumptions.
Sensitivity AnalysisSensitivity analysis shows how much a valuation, forecast, or risk metric changes when one input changes.

What to Check

  • Forecast source, valuation date, market data, accounting adjustments, and model version.
  • Cash-flow input, discount rate, multiple, growth assumption, terminal value, balance-sheet adjustment, and scenario range.
  • Comparable set, transaction set, sector, geography, size, leverage, margin profile, and accounting basis.
  • Effect on intrinsic value, relative value, price target, margin of safety, impairment view, deal price, or recommendation.
  • Sensitivity to growth, margins, reinvestment, discount rate, exit multiple, leverage, and market conditions.

Common Mistakes

  • Treating a valuation output as a precise fact instead of a range of estimates.
  • Comparing multiples without normalizing earnings, leverage, accounting policy, growth, and risk.
  • Ignoring valuation date, source quality, cyclicality, nonrecurring items, and sensitivity analysis.
  • Using valuation terminology as personalized investment, tax, legal, or appraisal advice.

Valuation content is educational and does not provide investment, tax, legal, accounting, appraisal, or valuation advice.

In this section

Choose a subsection first. Deeper term pages live inside each subsection, which keeps large topic hubs readable.

Heavy Tails

Heavy tails describe probability distributions with more extreme outcomes than a normal distribution, affecting risk and loss modeling.

Monte Carlo Simulation

Monte Carlo simulation estimates valuation or risk outcomes by running many randomized scenarios for uncertain inputs.

Probability Distribution

A probability distribution describes possible outcomes and their likelihoods, forming the basis for risk, return, and scenario modeling.

Scenario Analysis

Scenario analysis tests valuation, planning, or risk outcomes under coherent alternative sets of assumptions.

Sensitivity Analysis

Sensitivity analysis shows how much a valuation, forecast, or risk metric changes when one input changes.

Revised on Sunday, June 21, 2026
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