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Binary Options Calculator

Calculate the probability of price being over/under a target

Inputs

Current Price S
Target / Strike Price K
Time to Expiration T
Implied Volatility σ (annualized %)
Risk-Free Rate r (annualized %)

Probability

Probability OVER target
Price > 105
42.07%
Probability UNDER target
Price ≤ 105
57.93%
d2 Value
Standard deviations from strike
-0.20
Fair Value YES (Over)
$0.42
Fair Value NO (Under)
$0.58

Implied Volatility Reference

Asset / Market Typical IV Range Notes
S&P 500 (SPY) 12-20% Low vol environment; spikes to 30-40% in crashes
Nasdaq 100 (QQQ) 15-25% Slightly higher than SPY due to tech concentration
Individual Stocks 25-50% Varies widely; megacaps lower, growth stocks higher
Bitcoin (BTC) 40-80% High baseline; can spike 100%+ during volatility
Ethereum (ETH) 50-90% Generally higher than BTC
Altcoins 80-200% Extremely volatile; use with caution
Gold (GLD) 12-18% Low volatility safe haven
Crude Oil (USO) 25-45% Commodity volatility; spikes on geopolitical events
EUR/USD 6-10% Major FX pair; low vol
Treasury Bonds (TLT) 12-20% Rate-sensitive; higher in uncertain rate environments
Meme Stocks 80-300% GME, AMC etc; extreme IV during squeeze events
Earnings Events +15-40% Add this to baseline IV pre-earnings

How It Works

Uses the N(d2) formula from Black-Scholes for binary/digital options:

d2 = [ln(S/K) + (r - σ²/2) × T] / (σ × √T)

Where S = current price, K = strike, r = risk-free rate, σ = volatility, T = time in years.

P(over) = N(d2) = probability price finishes above strike
P(under) = 1 - N(d2) = probability price finishes at or below strike