BSM Price+Greeks
When to use: you already have model inputs (S or forward mark, K, T, r, σ) and need fair value + hedge ratios — not market-premium IV. European BSM price + analytic Greeks (delta, gamma, vega, theta, rho). Works for equity spots and power/commodity forwards (use the maturity mark as spot). USDC exact on Solana/Base. Free fixed sample: GET /v1/demo/option-price.
Offering
- Provider
- derivatives-pricer-production.up.railway.app
- Method
- POST
- Offering type
- Api Endpoint
- Transport type
- http
- Category
- Financial Analysis
- Delivery
- Not provided
- Pricing model
- Not provided
- x402 version
- 2
Endpoint context
- URL
https://derivatives-pricer-production.up.railway.app/v1/option/price- MIME type
- Not provided
- First seen
- 2026-10-16T01:50:45.949Z
- Last seen
- Tags
- options, black-scholes, greeks, multi-chain, USDC
Payment pricing
x402 payment terms are the authoritative price for calling this endpoint.
- Payment option 1
- 0.01 USDC
Atomic price: 10000 · Network: solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp · Asset: USDC · Scheme: exact - Payment option 2
- 0.01 USDC
Atomic price: 10000 · Network: eip155:8453 · Asset: USDC · Scheme: exact
Raw x402 terms
[
{
"scheme": "exact",
"network": "solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp",
"asset": "EPjFWdd5AufqSSqeM2qN1xzybapC8G4wEGGkZwyTDt1v",
"amount": "10000",
"payTo": "DCi9X5mmacNGLeJvCw9fdWgX3G8V4QquDn4EuXATkcYr"
},
{
"scheme": "exact",
"network": "eip155:8453",
"asset": "0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913",
"amount": "10000",
"payTo": "0x34cfb8bdbf16e4484b7da0ed31deed5771b16c8f"
}
]Observed health
- Status
- Healthy
- Latest latency
- 130 ms
- Average latency
- 112 ms
- HTTP status
- 204
- Last checked
- Reachability
- 100% over 15 checks
Latency is measured to the first response headers. A reachable result does not verify response accuracy or merchant identity.
Input schema
{
"additionalProperties": false,
"properties": {
"body": {
"additionalProperties": false,
"description": "European (default) or American option fair value. Legacy bodies use timeToExpiry year-fractions. Optional forwardStart+expiration (ISO-8601 with Z/offset) define a vol/exercise window; τ = years in that window (ACT/365.25), not calendar time from purchase. Not a swing/multi-exercise engine.",
"properties": {
"dividendYield": {
"description": "Continuous dividend / convenience / yield q (≥ 0, default 0).",
"examples": [
0,
0.02
],
"minimum": 0,
"type": "number"
},
"expiration": {
"description": "ISO-8601 end of vol/exercise window. Mutually exclusive with timeToExpiry.",
"format": "date-time",
"type": "string"
},
"forward": {
"description": "Forward mark F for model=black76 (preferred). If omitted, spot is used as F.",
"examples": [
100,
82.5
],
"exclusiveMinimum": 0,
"type": "number"
},
"forwardStart": {
"description": "ISO-8601 start of vol/exercise window. If ≤ now, behaves like plain option to expiration.",
"format": "date-time",
"type": "string"
},
"greekConvention": {
"default": "raw",
"description": "Greek units: \"raw\" (vega/1.0 vol, theta/year, rho/1.0 rate) or \"trading\" (vega/1%, theta/day, rho/bp).",
"enum": [
"raw",
"trading"
],
"type": "string"
},
"model": {
"default": "bsm",
"description": "Pricing model: \"bsm\" (default European BSM on spot) or \"black76\" (forward/futures).",
"enum": [
"bsm",
"black76"
],
"type": "string"
},
"optionStyle": {
"default": "european",
"description": "Exercise style (default \"european\"). American uses CRR binomial with early exercise.",
"enum": [
"european",
"american"
],
"type": "string"
},
"optionType": {
"description": "Call or put.",
"enum": [
"call",
"put"
],
"type": "string"
},
"rate": {
"description": "Continuously compounded risk-free rate r (e.g. 0.05 = 5%). For futures-style early exercise set r≈dividendYield.",
"examples": [
0.03,
0.05
],
"type": "number"
},
"spot": {
"description": "Underlying price S (> 0). Equity spot OR power/commodity forward mark for the option's window.",
"examples": [
100,
82.5,
45.5
],
"exclusiveMinimum": 0,
"type": "number"
},
"strike": {
"description": "Strike price K (> 0) in the same units as spot.",
"examples": [
100,
50
],
"exclusiveMinimum": 0,
"type": "number"
},
"timeToExpiry": {
"description": "Time to expiry T in years (≥ 0). Required unless expiration is set. Mutually exclusive with expiration.",
"examples": [
0.25,
1
],
"minimum": 0,
"type": "number"
},
"treeSteps": {
"description": "CRR steps for American (default 200 on single price).",
"maximum": 500,
"minimum": 50,
"type": "integer"
},
"volatility": {
"description": "Annualized volatility σ as a decimal (> 0). Applies over the vol-accrual window τ.",
"examples": [
0.15,
0.2,
0.45
],
"exclusiveMinimum": 0,
"type": "number"
}
},
"required": [
"spot",
"strike",
"rate",
"volatility",
"optionType"
],
"title": "OptionPriceRequest",
"type": "object"
},
"bodyType": {
"enum": [
"json",
"form-data",
"text"
],
"type": "string"
},
"method": {
"enum": [
"POST"
],
"type": "string"
},
"type": {
"const": "http",
"type": "string"
}
},
"required": [
"type",
"method",
"bodyType",
"body"
],
"type": "object"
}Output schema
{
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"input": {
"additionalProperties": false,
"properties": {
"body": {
"additionalProperties": false,
"description": "European (default) or American option fair value. Legacy bodies use timeToExpiry year-fractions. Optional forwardStart+expiration (ISO-8601 with Z/offset) define a vol/exercise window; τ = years in that window (ACT/365.25), not calendar time from purchase. Not a swing/multi-exercise engine.",
"properties": {
"dividendYield": {
"description": "Continuous dividend / convenience / yield q (≥ 0, default 0).",
"examples": [
0,
0.02
],
"minimum": 0,
"type": "number"
},
"expiration": {
"description": "ISO-8601 end of vol/exercise window. Mutually exclusive with timeToExpiry.",
"format": "date-time",
"type": "string"
},
"forward": {
"description": "Forward mark F for model=black76 (preferred). If omitted, spot is used as F.",
"examples": [
100,
82.5
],
"exclusiveMinimum": 0,
"type": "number"
},
"forwardStart": {
"description": "ISO-8601 start of vol/exercise window. If ≤ now, behaves like plain option to expiration.",
"format": "date-time",
"type": "string"
},
"greekConvention": {
"default": "raw",
"description": "Greek units: \"raw\" (vega/1.0 vol, theta/year, rho/1.0 rate) or \"trading\" (vega/1%, theta/day, rho/bp).",
"enum": [
"raw",
"trading"
],
"type": "string"
},
"model": {
"default": "bsm",
"description": "Pricing model: \"bsm\" (default European BSM on spot) or \"black76\" (forward/futures).",
"enum": [
"bsm",
"black76"
],
"type": "string"
},
"optionStyle": {
"default": "european",
"description": "Exercise style (default \"european\"). American uses CRR binomial with early exercise.",
"enum": [
"european",
"american"
],
"type": "string"
},
"optionType": {
"description": "Call or put.",
"enum": [
"call",
"put"
],
"type": "string"
},
"rate": {
"description": "Continuously compounded risk-free rate r (e.g. 0.05 = 5%). For futures-style early exercise set r≈dividendYield.",
"examples": [
0.03,
0.05
],
"type": "number"
},
"spot": {
"description": "Underlying price S (> 0). Equity spot OR power/commodity forward mark for the option's window.",
"examples": [
100,
82.5,
45.5
],
"exclusiveMinimum": 0,
"type": "number"
},
"strike": {
"description": "Strike price K (> 0) in the same units as spot.",
"examples": [
100,
50
],
"exclusiveMinimum": 0,
"type": "number"
},
"timeToExpiry": {
"description": "Time to expiry T in years (≥ 0). Required unless expiration is set. Mutually exclusive with expiration.",
"examples": [
0.25,
1
],
"minimum": 0,
"type": "number"
},
"treeSteps": {
"description": "CRR steps for American (default 200 on single price).",
"maximum": 500,
"minimum": 50,
"type": "integer"
},
"volatility": {
"description": "Annualized volatility σ as a decimal (> 0). Applies over the vol-accrual window τ.",
"examples": [
0.15,
0.2,
0.45
],
"exclusiveMinimum": 0,
"type": "number"
}
},
"required": [
"spot",
"strike",
"rate",
"volatility",
"optionType"
],
"title": "OptionPriceRequest",
"type": "object"
},
"bodyType": {
"enum": [
"json",
"form-data",
"text"
],
"type": "string"
},
"method": {
"enum": [
"POST"
],
"type": "string"
},
"type": {
"const": "http",
"type": "string"
}
},
"required": [
"type",
"method",
"bodyType",
"body"
],
"type": "object"
},
"output": {
"properties": {
"example": {
"description": "Fair value and Greeks. European Greeks are analytic BSM; American Greeks are finite-difference on the CRR tree. timeline.tauYears is the model life (window); calendarYearsToExpiry is purchase→expiry.",
"properties": {
"computedAt": {
"description": "ISO-8601 UTC timestamp of computation",
"type": "string"
},
"greeks": {
"description": "Greeks for hedge construction",
"properties": {
"delta": {
"description": "∂V/∂S",
"type": "number"
},
"gamma": {
"description": "∂²V/∂S²",
"type": "number"
},
"rho": {
"description": "∂V/∂r per 1.0 absolute rate",
"type": "number"
},
"theta": {
"description": "∂V/∂T per year",
"type": "number"
},
"vega": {
"description": "∂V/∂σ per 1.0 absolute vol",
"type": "number"
}
},
"required": [
"delta",
"gamma",
"vega",
"theta",
"rho"
],
"type": "object"
},
"greeksQuality": {
"enum": [
"analytic",
"finite-difference"
],
"type": "string"
},
"inputs": {
"description": "Echo of validated request inputs (timeToExpiry may be resolved τ)",
"type": "object"
},
"model": {
"enum": [
"black-scholes-merton",
"binomial-crr-american"
],
"type": "string"
},
"optionStyle": {
"enum": [
"european",
"american"
],
"type": "string"
},
"price": {
"description": "Model option fair value in underlying currency units",
"type": "number"
},
"requestId": {
"description": "Correlation id for this call",
"type": "string"
},
"timeline": {
"description": "Resolved ACT/365.25 window",
"type": "object"
},
"treeSteps": {
"type": "integer"
},
"units": {
"description": "Human/agent readable unit notes for price and Greeks",
"type": "object"
}
},
"required": [
"price",
"greeks",
"inputs",
"model",
"optionStyle",
"timeline",
"greeksQuality",
"requestId",
"computedAt"
],
"title": "OptionPriceResponse",
"type": "object"
},
"type": {
"type": "string"
}
},
"required": [
"type"
],
"type": "object"
}
},
"required": [
"input"
],
"type": "object"
}