TradingCalcCrypto 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.
Checked against QuantLib
The contract is a cash-or-nothing digital option, and QuantLib, the open-source quantitative finance library, prices those. On 3,000 random windows the probability here matches QuantLib to within 1e-11 percentage points. Details in the methodology docs.
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.
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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.