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Implied Probability Distribution - Risk-Neutral Probability from Options Prices
Method: Implied probabilities are calculated using the second derivative of option prices (butterfly spread approach).
The probability density at each strike is computed using finite differences for non-uniformly spaced strikes, then normalized to sum to 1.
Both call and put distributions are shown for comparison. They should theoretically match but may differ due to market microstructure, liquidity, and bid-ask spreads.
Calendar Spread Forward Volatility Analysis
This shows the forward implied volatility between two expiry dates, useful for trading calendar spreads.
Forward IV = sqrt((T2×IV2² - T1×IV1²) / (T2 - T1)), where T is time to expiry in years.
Forward Factor (FF) = (FrontIV - ForwardIV) / ForwardIV - measures the relative difference between front month and forward volatility.
FF > 0: Front month IV higher than forward period (backwardation). FF < 0: Forward period IV higher (contango).
Forward IV = sqrt((T2×IV2² - T1×IV1²) / (T2 - T1)), where T is time to expiry in years.
Forward Factor (FF) = (FrontIV - ForwardIV) / ForwardIV - measures the relative difference between front month and forward volatility.
FF > 0: Front month IV higher than forward period (backwardation). FF < 0: Forward period IV higher (contango).