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.
| Threshold | $ Level | Implied P |
|---|---|---|
| above -10% | $687.86 | 81.5% |
| above -5% | $726.08 | 74.9% |
| above spot | $764.29 | 56.4% |
| above +5% | $802.50 | 21.4% |
| above +10% | $840.72 | 0.0% |
| above +20% | $917.15 | 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.