Kresmion extracts risk-neutral probability densities from US options chains with the Breeden-Litzenberger method and reports the cumulative probability at standard strike thresholds for each expiry.
For each ticker and expiry the out-of-the-money option prices are turned into implied volatilities, a smooth volatility curve is fitted, call prices are rebuilt from it and their second derivative (Breeden-Litzenberger) gives the risk-neutral probability density. The cumulative tail probabilities show what the market charges for moves above and below the current price.
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 (for example, options markets price tail risk higher than its historical frequency).
| Threshold | $ Level | Implied P |
|---|---|---|
| above -10% | $692.64 | 99.7% |
| above -5% | $731.12 | 97.7% |
| above spot | $769.60 | 57.9% |
| above +5% | $808.08 | 0.2% |
| above +10% | $846.56 | 0.0% |
| above +20% | $923.52 | 0.0% |
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.