Options Pricing

Probability of Profit

Black-Scholes PoP for any options trade

What is Probability of Profit?

Probability of Profit (PoP) estimates the likelihood that an options trade will be profitable at expiration, derived from the Black-Scholes model using the option's delta. For a short put at delta 0.20, the PoP is approximately 80% (1 − delta). For a short strangle combining a 0.20-delta put and a 0.20-delta call, the combined PoP is approximately 60%. This is a theoretical model probability based on current implied volatility, not a historical backtest. Fat-tailed real-world distributions mean actual win rates can differ significantly. Professional options traders use PoP as a starting screen, combining it with expected value (premium received × PoP − max loss × (1−PoP)) for position sizing decisions.

Formula

PoP (short option) ≈ 1 − |Delta| × 100%

Delta from Black-Scholes: Δ_call = N(d₁)

d₁ = [ln(S/K) + (r + σ²/2)×T] / (σ×√T)

For a short strangle: PoP ≈ N(d₁_call) − N(d₁_put) × 100%

Calculator

Stock Price ($)Strike ($)Days to ExpiryRisk-Free Rate (%)Implied Volatility (%)

How to Use

1
Enter BS inputs: Stock price, strike, DTE, risk-free rate, IV.
2
Choose position: Short put, short call, or short strangle (two strikes).
3
Read PoP: The probability the position expires profitable. A 0.20-delta short put has ~80% PoP.
4
Combine with EV: High PoP alone is insufficient: compare premium collected to maximum loss to assess expected value.

Worked Example

Example: Short put with delta 0.20

Delta

0.20

Premium

$1.50

Strike

$140

PoP ≈ 1 − 0.20 = 80%. You win 80% of the time but risk $138.50 (strike − premium) to make $1.50. Expected Value ≈ (0.80 × $1.50) − (0.20 × $138.50) = $1.20 − $27.70 = negative EV. High PoP does not guarantee positive EV, so position sizing and stop losses are essential.