Option-Implied Probabilities vs Normal Distribution Models

Textbook models assume a tidy bell curve. Option prices reveal what traders actually believe — and it is lumpier, fatter-tailed and more lopsided than the textbook.

Two ways to produce a probability

A statistical model starts from an assumption about the shape of returns — usually lognormal — estimates volatility from history, and computes probabilities analytically. It is transparent, cheap, and requires only price history.

An option-implied distribution works backwards from market prices across many strikes. Because option prices at every strike collectively describe how much traders will pay for each region of outcomes, the full distribution can be extracted from them.

What the market's distribution actually looks like

It is not normal, and the deviations are systematic. Tails are fatter than the lognormal assumption, because extreme moves genuinely occur more often than the bell curve allows.

It is skewed, typically with more weight on the downside for equity indices — the same phenomenon visible as volatility skew. And around known catalysts it can become bimodal, with probability mass concentrated at two separate outcomes rather than smoothly around one centre, which no single-volatility model can represent.

Where each approach wins

Option-implied distributions are richer and forward-looking. They know about the earnings date and the policy meeting. Their drawbacks are practical: they need liquid options across many strikes, they are noisy when volume is thin, and they embed the variance risk premium, which inflates the apparent probability of large moves.

Statistical models are unbiased in that respect, work on any instrument with price history, and are entirely reproducible. Their weakness is that they are blind to the calendar and, in their simplest form, symmetric.

When a simple model is good enough

For a broad, liquid index over a short-to-medium horizon with no scheduled catalyst inside the window, a lognormal model with a well-estimated volatility is a reasonable approximation. The distribution is close enough to normal in the central region that the error is small where most outcomes land.

It becomes unreliable in exactly three situations: when a discrete catalyst falls inside the horizon, when you care specifically about the tails rather than the middle, and when the asset has strongly asymmetric risk. In those cases the shape of the distribution matters more than the width, and a symmetric model cannot express it.

The honest approach is to treat a statistical model as a disciplined baseline and to know precisely which of its assumptions is likely to be violated in the case in front of you.