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The probability layer turns fitted volatility into probabilities over future prices. It answers questions such as: what probability does the options market imply that a stock will be above $100 at next week’s expiry?

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Risk-neutral probabilities

OIPD returns risk-neutral probabilities. They are not real-world forecasts. They are probabilities consistent with option prices after discounting and the chosen pricing assumptions.

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Curve or surface

ProbCurve is for one expiry. ProbSurface is for many expiries. You can build probability objects directly from chains: 
from oipd import ProbCurve

prob = ProbCurve.from_chain(chain, market)
print(prob.prob_below(100))
Or you can fit volatility first and convert it: 
from oipd import VolCurve

vol = VolCurve().fit(chain, market)
prob = vol.implied_distribution()
The second path is useful when you want to inspect the volatility fit before using the probabilities.

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PDF and CDF

The probability layer exposes two standard views: the PDF and the CDF. The PDF is the probability density function. It shows where probability is concentrated across possible future prices. A higher PDF value around 100meansmoreprobabilitymassissittingnear100 means more probability mass is sitting near 100 than near prices with lower density. The CDF is the cumulative distribution function. It answers a direct threshold question: what is the probability that the future price ends below this level? 
prob.pdf(100)
prob.prob_below(100)
prob.prob_between(90, 110)
prob.quantile(0.5)
quantile(0.5) returns the median price under the fitted risk-neutral distribution.

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Across time

ProbSurface lets you ask the same questions at different maturities: 
from oipd import ProbSurface

surface = ProbSurface.from_chain(chain, market)
prob_45d = surface.cdf(100, t=45 / 365)
You can also extract one date as a ProbCurve: 
curve = surface.slice(surface.expiries[0])
curve.prob_below(100)

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Diagnostics

Probability calculations can expose numerical issues, especially around CDF monotonicity. By default, OIPD uses cdf_violation_policy="warn": it repairs material monotonicity issues and records warnings. Use cdf_violation_policy="raise" when you prefer the calculation to fail instead. Inspect .warning_diagnostics on fitted probability objects when results need review.