Heavy Tails
Heavy tails assign more weight to extreme financial outcomes; their shape affects loss estimates, model choice, and whether means and variances are finite.
Distributions, simulations, scenarios, and sensitivity tests reveal different aspects of financial uncertainty, including input dependence and adverse outcomes.
Financial uncertainty involves more than choosing a single expected cash flow or valuation. A probability distribution assigns likelihoods to outcomes; its average does not fully describe downside risk. Heavy tails explain why extreme losses need separate attention and why not every model has a finite variance.
Sensitivity analysis examines input effects and decision thresholds. Scenario analysis evaluates coherent alternative conditions. Neither automatically assigns probabilities to the cases tested.
Stochastic modeling specifies probability distributions and dependence assumptions. Monte Carlo simulation evaluates such a model through repeated sampling. The method should match the financial question, including whether the purpose is forecasting, risk estimation, or pricing.
Read the assumptions alongside every result. Tail behavior, shared exposures, cash-flow timing, and omitted risks can matter more than extra decimal places. These articles provide financial education, not guaranteed forecasts or personalized investment recommendations.
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Heavy tails assign more weight to extreme financial outcomes; their shape affects loss estimates, model choice, and whether means and variances are finite.
Monte Carlo simulation uses repeated random sampling to estimate financial outcomes; results depend on distributions, dependence, and valuation assumptions.
A probability distribution assigns likelihoods to financial outcomes, helping distinguish expected loss, loss thresholds, and uncertainty in risk models.
Scenario analysis compares financial results under coherent alternative assumptions, revealing downside exposure without treating cases as forecasts.
Sensitivity analysis tests how financial results respond to changed inputs, using one-way tests, two-way tables, or broader methods to identify key drivers.