modelimplied

Modelimplied, often written as model-implied, refers to quantities whose values are dictated by a statistical, econometric, or financial model given its structure and estimated parameters, rather than directly observed from data. These quantities represent what the model predicts about unobserved variables, future outcomes, or latent aspects of the system under study.

Calculation: To obtain model-implied values, one applies the model's equations to the estimated parameters and the observed inputs. This yields conditional distributions, expected values, or moments for outcomes of interest. In practice, model-implied figures are compared with empirical estimates to assess model fit or to derive prices, probabilities, or risk metrics consistent with the model.

Examples: In finance, model-implied volatility is the volatility value that a pricing model assigns to an option given its market price. In credit risk, a model-implied probability of default is the probability of default produced by a structural or reduced-form model. In macroeconomics, model-implied paths for inflation or output are the trajectories implied by a forecasting model under current parameter estimates.

Uses and limitations: Model-implied quantities are useful for validation, scenario analysis, and pricing. They depend on the correctness of the model and parameter estimates; misspecification, estimation error, or structural breaks can cause model-implied figures to diverge from observed data. Analysts often examine discrepancies between model-implied and empirical metrics to diagnose model risk.

Related concepts include implied volatility, model-based inference, structural models, and model calibration.