Probability of finishing ITM API

Compute the lognormal (Black-Scholes) probability an option finishes in-the-money: P(ITM call) = N(d2), P(ITM put) = N(-d2), with d2 = [ln(S/K) + (r - q - σ²/2)T] / (σ√T), via a deterministic normal-CDF approximation. Answers 'what's the probability this call expires ITM','what are the odds my put finishes in the money','what's N(d2) for this option'.

Price$0.03per request

MethodPOST

Route/v1/calc/opt-probability-itm

StatusLive

MIME typeapplication/json

Rate limit120/minute

CacheNo cache

optionsprobability-itmcalcblack-scholesn-d2volatilityderivativestrading

API URLhttps://x402.hexl.dev/v1/calc/opt-probability-itm

Integration docs

Example request

{
  "type": "call",
  "underlying": 100,
  "strike": 105,
  "impliedVolatility": 0.3,
  "timeToExpiryYears": 0.25,
  "rate": 0.02
}

Example response

{
  "type": "call",
  "underlying": 100,
  "strike": 105,
  "impliedVolatility": 0.3,
  "timeToExpiryYears": 0.25,
  "rate": 0.02,
  "dividendYield": 0,
  "d2": -0.366934,
  "probabilityItm": 0.356834,
  "probabilityItmPercent": 35.6834,
  "probabilityOtmPercent": 64.3166,
  "formula": "P(ITM call)=N(d2), d2=[ln(S/K)+(r-q-σ²/2)T]/(σ√T)"
}

Input schema

{
  "type": "object",
  "required": [
    "type",
    "underlying",
    "strike",
    "impliedVolatility",
    "timeToExpiryYears"
  ],
  "properties": {
    "type": {
      "type": "string",
      "enum": [
        "call",
        "put"
      ]
    },
    "underlying": {
      "type": "number",
      "examples": [
        100
      ]
    },
    "strike": {
      "type": "number",
      "examples": [
        105
      ]
    },
    "impliedVolatility": {
      "type": "number",
      "description": "annualized IV as a decimal",
      "examples": [
        0.3
      ]
    },
    "timeToExpiryYears": {
      "type": "number",
      "examples": [
        0.25
      ]
    },
    "rate": {
      "type": "number",
      "description": "risk-free rate (decimal)",
      "default": 0,
      "examples": [
        0.02
      ]
    },
    "dividendYield": {
      "type": "number",
      "default": 0
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}