Crypto Up/Down Fair Value Calculator
DIGITAL-OPTION PRICING · TIME-WINDOWED CONTRACTS · THEORETICAL, NOT A LIVE QUOTE
Compute the theoretical fair value of a crypto up/down window contract (ADI Predictstreet, Kalshi-style dailies) using the same math options traders use to price a digital option.
Volatility is the one input this tool can't fetch for you — there's no live market on these contracts yet to read an implied vol from (see the guide below). Getting it wrong matters most on short windows: a small vol error swings the probability a lot near the reference price.
What is a crypto up/down fair value?
Venues like ADI Predictstreet and Kalshi list "up or down" contracts: pick a coin, a reference price pinned at the window's open, and a close time — the contract pays out based on whether the settlement price finishes at/above or below that reference. That's structurally a cash-or-nothing digital option: strike = the reference price, expiry = the window close, underlying = the coin's spot price. This tool computes what that contract is theoretically worth right now, using the same math options traders use to price a digital option — not a read of any venue's actual quoted price.
The formula
- d1 = (ln(S/K) + (r + vol² / 2) × T) / (vol × √T)
- d2 = d1 − vol × √T
- P(finishes above K) = N(d2) — the standard normal CDF
- P(finishes below K) = 1 − N(d2)
S is the current price, K the reference/pinned price, T the time to close (in years), vol the annualized volatility, r the risk-free rate (negligible for these short windows, defaults to 0).
Worked example
BTC is at $90,000, the window's reference is also $90,000 (at-the-money), 60 minutes to close, 50% annualized volatility:
- d2 ≈ −0.00267
- P(above) = N(−0.00267) ≈ 49.89%
- P(below) ≈ 50.11%
Even exactly at the money, the fair probability isn't precisely 50/50 — under the standard risk-neutral pricing assumption, the median outcome drifts a hair below the starting price when the risk-free rate is 0. That small asymmetry is a real property of the math, not rounding error.
Why this exists: no live price to read yet
This tool exists because ADI Predictstreet's crypto up/down markets are real and publicly readable, but — checked live — currently have empty order books and zero trades on every window size. There's no actual market price to quote. Rather than show a meaningless 50/50 placeholder as if it were real, this computes what a rational fair price would be, the same way Black-Scholes prices an option independent of whether it's actively traded. If a venue's real quoted price ever diverges a lot from this number, that's either a genuine edge or a sign your volatility input needs revisiting — volatility is the one input this tool can't fetch for you.
Where to go next
Already have a live market price and just want to convert it to odds? Probability Calculator. Want the market's own live implied view across a full price ladder instead of one threshold? Market-Implied Odds.
Use via API or MCP
This calculation is available as a deterministic API call — useful for bots or AI agents pricing time-windowed crypto contracts before a real market price exists for them.
What is a "crypto up/down" contract?
A binary contract that pays out based on whether a coin's price is above or below a reference price (pinned when the window opens) by a fixed close time — ADI Predictstreet and Kalshi both list these, in windows from 5 minutes to a full day.
Why can't I just read the live market price instead of computing it?
Some venues' up/down contracts have real trading and a live price. Others — checked live for ADI Predictstreet's crypto vertical — currently have zero trades and an empty order book on every window, so there's no real price to read yet. This tool computes what a rational price should be instead.
Where does the volatility number come from?
You enter it. Unlike a liquid options market, there's no live implied-volatility quote to pull from these contracts, so this is the one honest assumption in the calculation — and the one most worth double-checking, especially on short windows.
Why isn't the fair probability exactly 50% when the price equals the reference?
Under the standard risk-neutral pricing model, the median outcome drifts slightly below the starting price at a 0% risk-free rate — a small, real asymmetry in the math (about 49.89% vs 50.11% in the worked example above), not an error.