# Breeden-Litzenberger

*Quant & Pricing — Finicade finance glossary*

Breeden-Litzenberger extracts the market implied probability distribution from option prices: the second derivative of price by strike is the density.

Breeden-Litzenberger extracts the market's implied probability distribution from option prices: the second derivative of price with respect to strike is the risk-neutral density. It means a full options chain tells you not just expected level but the market's entire probability view, including how fat it thinks the tails are. The practical obstacle is that differentiating twice amplifies noise, so the surface must be smoothed carefully first.

**Also known as:** implied distribution, risk-neutral density, Breeden Litzenberger formula

**Related terms:** [Volatility Surface](https://finicade.com/glossary/volatility-surface), [Probability Distribution](https://finicade.com/glossary/probability-distribution), [Risk-Neutral Pricing](https://finicade.com/glossary/risk-neutral-pricing), [Binary Option](https://finicade.com/glossary/binary-options), [Fat Tails](https://finicade.com/glossary/fat-tails)

**Taught in:** Quant Quest — Stochastic Calculus II

Source: https://finicade.com/glossary/breeden-litzenberger