Kresmion / Tools

Risk-Neutral Implied Probability

Decoding available US options chains into the probability distribution the market is currently pricing. For each ticker/expiry we fit a smooth call-price curve, take its second derivative (Breeden-Litzenberger), and discount to get the risk-neutral probability density. The cumulative tail probabilities show what the market charges for upside / downside scenarios.

Important: These are risk-neutral probabilities, which bake in the risk premium investors demand. They are NOT predictions or the market's "real-world" expectations. Real-world probabilities differ systematically (e.g. options markets price tail risk higher than its historical frequency).
12 DTE
Risk-neutral PDF: SPY on 2026-09-25
spot $764.29 · 130/142 liquid strikes · r=4.00%
Cumulative probability above level
Threshold$ LevelImplied P
above -10%$687.8681.5%
above -5%$726.0874.9%
above spot$764.2956.4%
above +5%$802.5021.4%
above +10%$840.720.0%
above +20%$917.150.0%
1-σ implied move (16th to 84th percentile)
±17.0%
≈ ±$129.85 from spot
The market is currently pricing roughly a 68% probability that SPY closes within ±17.0% of its current price ($764.29) by 2026-09-25. Distribution integrates to 1.893 pre-normalisation (tolerance 1.0 ± 0.10).

Understand options positioning

Connect the definitions to a dated SPY gamma snapshot. Dealer exposure is modeled from options data; the sign and size depend on the stated assumptions.

Primary-source background: Options Industry Council: gamma. Kresmion methodology and limitations.