Learn / price an option

Price a European call

Change a sample market input. Price and Greeks use Black–Scholes–Merton, with explicit decimal rates and years to expiry.

Try it

Sample data

Change a sample market input. Price and Greeks use Black–Scholes–Merton, with explicit decimal rates and years to expiry.

Call price2.3909USD / share

Delta0.3677

Gamma0.0377

Vega0.1884per 1% volatility

Price across underlying prices

European callOption price · USD / share

Exact chart data

Series	Underlying price · USD	Option price · USD / share
European call	70	0.00007436772427411604
European call	71	0.00013834634551955754
European call	72	0.0002506011453697714
European call	73	0.00044248041148476497
European call	74	0.0007623304942515619
European call	75	0.0012827848346888895
European call	76	0.0021102324290399183
European call	77	0.003396723103711738
European call	77.99999999999999	0.005354446682725472
European call	78.99999999999999	0.008272745172492157
European call	80	0.012537384939741547
European call	81	0.01865154134933955
European call	82	0.027257651892743873
European call	83	0.039159003403250514
European call	84	0.0553396674468003
European call	85	0.07698121964691174
European call	86	0.10547460472891901
European call	87	0.14242556307595544
European call	87.99999999999999	0.18965222876583088
European call	88.99999999999999	0.24917384152762256
European call	89.99999999999999	0.3231899689659805
European call	90.99999999999999	0.4140501799354084
European call	92	0.5242147031873543
European call	93	0.6562071986657614
European call	94	0.812561311835502
European call	95	0.9957631277694219
European call	96	1.2081919536772041
European call	97	1.4520620108674542
European call	98	1.729367599188528
European call	99	2.041834113337103
European call	100	2.3908769595711306
European call	101	2.777569973233703
European call	102	3.2026244098542804
European call	103	3.6663790170210575
European call	104	4.1688011320720335
European call	104.99999999999999	4.7094982294731835
European call	106	5.287738892448992
European call	106.99999999999999	5.902481828412654
European call	108	6.552411300078745
European call	108.99999999999999	7.235977207678516
European call	110.00000000000001	7.951438027980856
European call	110.99999999999999	8.696904881597817
European call	111.99999999999999	9.470385145137655
European call	112.99999999999999	10.269824229996104
European call	113.99999999999999	11.093144394734864
European call	114.99999999999999	11.938279723415604
European call	115.99999999999999	12.803206670189681
European call	117	13.685969825923578
European call	118	14.58470279405789
European call	119	15.497644262149834
European call	120	16.423149517923576
European call	121	17.359697782473887
European call	122	18.305895819404213
European call	123	19.260478329963732
European call	124	20.222305664894137
European call	125	21.190359378740183
European call	126	22.163736127194838
European call	127	23.141640367952405
European call	127.99999999999999	24.123376275479032
European call	129	25.108339224460252
European call	129.99999999999997	26.096007139132027

Assumptions & conventions

{
  "price": {
    "conventionsVersion": "0.0.1",
    "dayCount": "ACT/365F",
    "compounding": "continuous",
    "timeToExpiryYears": 0.25,
    "dividendModel": "none",
    "units": {
      "theta": "perDay",
      "vega": "per1Percent",
      "rho": "per1Percent"
    },
    "model": "black-scholes-merton",
    "engine": "black-scholes-merton"
  },
  "greeks": {
    "conventionsVersion": "0.0.1",
    "dayCount": "ACT/365F",
    "compounding": "continuous",
    "timeToExpiryYears": 0.25,
    "dividendModel": "none",
    "units": {
      "theta": "perDay",
      "vega": "per1Percent",
      "rho": "per1Percent"
    },
    "model": "black-scholes-merton",
    "engine": "black-scholes-merton"
  }
}

Diagnostics & warnings

{
  "price": {
    "engine": "black-scholes-merton",
    "method": "closed-form",
    "converged": true,
    "warnings": []
  },
  "greeks": {
    "engine": "black-scholes-merton",
    "method": "closed-form",
    "converged": true,
    "warnings": []
  }
}

Full result · JSON

{
  "price": {
    "value": 2.3908769595711306,
    "assumptions": {
      "conventionsVersion": "0.0.1",
      "dayCount": "ACT/365F",
      "compounding": "continuous",
      "timeToExpiryYears": 0.25,
      "dividendModel": "none",
      "units": {
        "theta": "perDay",
        "vega": "per1Percent",
        "rho": "per1Percent"
      },
      "model": "black-scholes-merton",
      "engine": "black-scholes-merton"
    },
    "diagnostics": {
      "engine": "black-scholes-merton",
      "method": "closed-form",
      "converged": true,
      "warnings": []
    }
  },
  "greeks": {
    "value": {
      "delta": 0.3677186551805255,
      "gamma": 0.03768050654865944,
      "theta": -0.0244146324714278,
      "vega": 0.1884025327432972,
      "rho": 0.08595247139620354
    },
    "assumptions": {
      "conventionsVersion": "0.0.1",
      "dayCount": "ACT/365F",
      "compounding": "continuous",
      "timeToExpiryYears": 0.25,
      "dividendModel": "none",
      "units": {
        "theta": "perDay",
        "vega": "per1Percent",
        "rho": "per1Percent"
      },
      "model": "black-scholes-merton",
      "engine": "black-scholes-merton"
    },
    "diagnostics": {
      "engine": "black-scholes-merton",
      "method": "closed-form",
      "converged": true,
      "warnings": []
    }
  },
  "priceCurve": [
    {
      "x": 70,
      "y": 0.00007436772427411604
    },
    {
      "x": 71,
      "y": 0.00013834634551955754
    },
    {
      "x": 72,
      "y": 0.0002506011453697714
    },
    {
      "x": 73,
      "y": 0.00044248041148476497
    },
    {
      "x": 74,
      "y": 0.0007623304942515619
    },
    {
      "x": 75,
      "y": 0.0012827848346888895
    },
    {
      "x": 76,
      "y": 0.0021102324290399183
    },
    {
      "x": 77,
      "y": 0.003396723103711738
    },
    {
      "x": 77.99999999999999,
      "y": 0.005354446682725472
    },
    {
      "x": 78.99999999999999,
      "y": 0.008272745172492157
    },
    {
      "x": 80,
      "y": 0.012537384939741547
    },
    {
      "x": 81,
      "y": 0.01865154134933955
    },
    {
      "x": 82,
      "y": 0.027257651892743873
    },
    {
      "x": 83,
      "y": 0.039159003403250514
    },
    {
      "x": 84,
      "y": 0.0553396674468003
    },
    {
      "x": 85,
      "y": 0.07698121964691174
    },
    {
      "x": 86,
      "y": 0.10547460472891901
    },
    {
      "x": 87,
      "y": 0.14242556307595544
    },
    {
      "x": 87.99999999999999,
      "y": 0.18965222876583088
    },
    {
      "x": 88.99999999999999,
      "y": 0.24917384152762256
    },
    {
      "x": 89.99999999999999,
      "y": 0.3231899689659805
    },
    {
      "x": 90.99999999999999,
      "y": 0.4140501799354084
    },
    {
      "x": 92,
      "y": 0.5242147031873543
    },
    {
      "x": 93,
      "y": 0.6562071986657614
    },
    {
      "x": 94,
      "y": 0.812561311835502
    },
    {
      "x": 95,
      "y": 0.9957631277694219
    },
    {
      "x": 96,
      "y": 1.2081919536772041
    },
    {
      "x": 97,
      "y": 1.4520620108674542
    },
    {
      "x": 98,
      "y": 1.729367599188528
    },
    {
      "x": 99,
      "y": 2.041834113337103
    },
    {
      "x": 100,
      "y": 2.3908769595711306
    },
    {
      "x": 101,
      "y": 2.777569973233703
    },
    {
      "x": 102,
      "y": 3.2026244098542804
    },
    {
      "x": 103,
      "y": 3.6663790170210575
    },
    {
      "x": 104,
      "y": 4.1688011320720335
    },
    {
      "x": 104.99999999999999,
      "y": 4.7094982294731835
    },
    {
      "x": 106,
      "y": 5.287738892448992
    },
    {
      "x": 106.99999999999999,
      "y": 5.902481828412654
    },
    {
      "x": 108,
      "y": 6.552411300078745
    },
    {
      "x": 108.99999999999999,
      "y": 7.235977207678516
    },
    {
      "x": 110.00000000000001,
      "y": 7.951438027980856
    },
    {
      "x": 110.99999999999999,
      "y": 8.696904881597817
    },
    {
      "x": 111.99999999999999,
      "y": 9.470385145137655
    },
    {
      "x": 112.99999999999999,
      "y": 10.269824229996104
    },
    {
      "x": 113.99999999999999,
      "y": 11.093144394734864
    },
    {
      "x": 114.99999999999999,
      "y": 11.938279723415604
    },
    {
      "x": 115.99999999999999,
      "y": 12.803206670189681
    },
    {
      "x": 117,
      "y": 13.685969825923578
    },
    {
      "x": 118,
      "y": 14.58470279405789
    },
    {
      "x": 119,
      "y": 15.497644262149834
    },
    {
      "x": 120,
      "y": 16.423149517923576
    },
    {
      "x": 121,
      "y": 17.359697782473887
    },
    {
      "x": 122,
      "y": 18.305895819404213
    },
    {
      "x": 123,
      "y": 19.260478329963732
    },
    {
      "x": 124,
      "y": 20.222305664894137
    },
    {
      "x": 125,
      "y": 21.190359378740183
    },
    {
      "x": 126,
      "y": 22.163736127194838
    },
    {
      "x": 127,
      "y": 23.141640367952405
    },
    {
      "x": 127.99999999999999,
      "y": 24.123376275479032
    },
    {
      "x": 129,
      "y": 25.108339224460252
    },
    {
      "x": 129.99999999999997,
      "y": 26.096007139132027
    }
  ]
}

Use it in your project

Returns a number: the option price in USD per share. No array conversion or chart setup is needed. Use blackScholes.greeks(input) for a named Greeks object, or .explain(input) for assumptions and diagnostics.

import { blackScholes } from '@insiderfinance/totalfinance/options';

const input = {
  "type": "call",
  "spot": 100,
  "strike": 105,
  "timeToExpiryYears": 0.25,
  "volatility": 0.2,
  "riskFreeRate": 0.04,
  "dividendYield": 0
} as const;
const result = blackScholes.price(input);
console.log(result);

Output of this example

2.3908769595711306

Reproduce this entire playground

This complete example reproduces every chart point and the full playground result. Sample generation and chart mapping are example setup, not required conversions of library outputs.

import { blackScholes } from '@insiderfinance/totalfinance/options';

const input = {
  "type": "call",
  "spot": 100,
  "strike": 105,
  "timeToExpiryYears": 0.25,
  "volatility": 0.2,
  "riskFreeRate": 0.04,
  "dividendYield": 0
} as const;
const priceCurve = Array.from({ length: 61 }, (_, index) => {
  const spot = input.spot * (0.7 + index / 100);
  return { x: spot, y: blackScholes.price({ ...input, spot }) };
});
const result = {
  price: blackScholes.price.explain(input),
  greeks: blackScholes.greeks.explain(input),
  priceCurve,
};
console.log(result);

Both examples use the last successfully calculated inputs. The first call may show fewer scenarios or selected report fields, as labeled above. Displayed metrics are rounded; copied calculations retain exact values.

Continue with the full API reference or the API levels guide.