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Black Scholes

black_scholes
Read-onlyIdempotent

European option pricing (Black-Scholes-Merton with continuous dividend yield): call and put prices, delta, gamma, vega, theta per day, rho, d1/d2 and probability of finishing in the money; with a market price it solves implied volatility. Works for equity, index and crypto options (set the yield to 0). Price: $0.002 USDC per successful call (x402, Solana). Same tool over HTTPS: GET https://scorptech.it.com/api/x402/v1/black-scholes

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "spot": "<spot>",
      "strike": "<strike>",
      "daysToExpiry": "<daysToExpiry>"
    },
    "name": "black_scholes"
  }
}

Input Schema

NameRequiredDescriptionDefault
spotYesUnderlying price
typeNoboth
strikeYes
ratePctNoRisk-free rate, continuous, percent
marketPriceNoOption market price: solve implied volatility (needs type call or put)
daysToExpiryYesCalendar days to expiry (year = 365)
volatilityPctNoAnnualised volatility in percent (not needed when solving implied vol)
dividendYieldPctNo

Schema Changelog

Changes observed during successful MCP inspections.

  1. Added

TDQS

A4.2/5.0
Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already cover read-only, idempotent, non-destructive, open-world semantics, so the description's main job is disclosing operational traits. It does this well: cost of $0.002 USDC per successful call via x402 on Solana, and an equivalent HTTPS endpoint, which materially affects how an agent should invoke it. It stops short of error/failure behavior, hence a 4 rather than 5.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

It is a single dense paragraph that front-loads the core computation before moving to implied vol, asset applicability, and payment details. It's slightly run-on but every clause carries information; nothing is filler.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

With no output schema and 8 parameters, the description compensates by enumerating the returned greeks and probabilities and explaining the implied-volatility mode. Combined with annotations covering safety and the explicit payment model, an agent has everything needed to call it correctly.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 63%, so the schema already documents most parameters (spot, ratePct, marketPrice, daysToExpiry, volatilityPct). The description adds marginal value by clarifying that 'yield to 0' applies to crypto/equity and by framing the implied-vol path, but it doesn't explain the undocumented 'type' or 'dividendYieldPct' fields in depth, so a baseline 3 is appropriate.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description names the specific model (Black-Scholes-Merton with continuous dividend yield) and enumerates exactly what it computes: call/put prices, delta, gamma, vega, theta per day, rho, d1/d2, probability of finishing ITM, plus implied volatility solving. This is far more specific than the generic name and clearly distinguishes it from other finance siblings like bond_calc or portfolio_metrics.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

It states concrete usage conditions: set dividend yield to 0 for equity/index/crypto, supply a marketPrice with type call or put to solve implied volatility, and omit volatility in that case. It doesn't name a competing sibling or explicitly say when NOT to use it, but the domain is narrow enough that the conditions given are actionable.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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