Bitcoin Contract Greeks
An interactive Bachelier visualiser for a Kalshi-style cash-or-nothing binary on Bitcoin — will BTC be above $K in t hours? Terminal price is normal around spot, so fair value is simply the probability of finishing in the money, quoted in cents. Drag the spot handle along the curve and the four greeks update live.
Volatility is quoted the way the model wants it: an annualised normal vol in dollars per √year, held fixed while spot moves. Beside the input it is also given as a percentage of spot a year, the way options markets quote it. Everything on this page is closed-form — no simulation, no fitting.
Prices are undiscounted probabilities — Kalshi pays interest on funds, so positions earn the risk-free rate automatically. No discounting, no rho.
Drag anywhere on the chart to move spot; the chart re-centres when you let go, so drag again to go further. The handle is focusable — arrow keys nudge $100, Shift $1,000.
As expiry approaches, the curve sharpens into a step — delta near the strike explodes (pin risk).
Value change per move in BTC. For a binary, delta is the probability density of expiring exactly at the strike (its negative for Below) — it spikes near the strike close to expiry (pin risk).
How fast delta changes. For Above, positive below the strike and negative above it (the reverse for Below); exactly zero at the money.
Value drift per hour as time passes. In-the-money binaries gain toward $1, out-of-the-money decay toward $0 — equal to −½s²Γ exactly (the heat equation).
Sensitivity to annualised normal vol. Out-of-the-money is long vol, in-the-money is short vol, exactly zero at the money.
Greek profile
Gamma, theta and vega all cross zero exactly at the strike and peak one terminal standard deviation away — everything dangerous lives at d = ±1.