Risk-neutral density

Estimated terminal price distribution for Oct 16, 2026, normalized to total probability 1 across the quoted strike range.

Spot

$578.40

Expected

$579.35

Median

$580.16

Mode

$580.80

5th pct

$543.29

95th pct

$612.92

Density with reference levels

Strike range $480 – $640 · 401 grid points

Read any probability directly off the curve

Smoothing strength0.055

Gaussian kernel bandwidth in log-moneyness

Risk-free rate4.30%

Continuous discount rate r

Dividend yield1.30%

Continuous yield q

Density = e^rT · ∂²C/∂K², evaluated as a central second difference of the Black-Scholes call curve refitted from the smoothed smile.
0 grid point(s) came out negative from residual curvature noise and were clipped to zero before normalization.
Total probability outside the quoted strike range is truncated, so tail probabilities are lower bounds. Implied 1σ move: ±3.7%.