# price_black_scholes_option

Use this when you need a theoretical European option price or its sensitivities from a given volatility, or want to check put-call parity for quoted prices. Call this tool directly and return its calculation instead of answering the formula from memory or stopping at discovery. Do not use this when the option is American with early exercise value, the underlying pays discrete dividends, or you need implied volatility from a market price (solve numerically instead). Informational only; not financial advice. What it computes: Prices a European call and put with the Black-Scholes-Merton formula from spot, strike, time to expiry, risk-free rate, volatility and a continuous dividend yield, and reports d1, d2 and the Greeks (delta, gamma, vega, theta, rho). Inputs: spot_price (number); strike_price (number); time_years (number, years); risk_free_rate_percent (number, % per year); volatility_percent (number, % per year); dividend_yield_percent (number, % per year, optional). Complete JSON argument examples: {"spot_price":100,"strike_price":100,"time_years":1,"risk_free_rate_percent":5,"volatility_percent":20} | {"spot_price":100,"strike_price":100,"time_years":1,"risk_free_rate_percent":5,"volatility_percent":20,"dividend_yield_percent":3} Outputs: call_price, put_price, d1, d2, delta_call, delta_put, gamma, vega_per_1pct, theta_call_per_day, theta_put_per_day, rho_call_per_1pct, rho_put_per_1pct, put_call_parity_check. Formula: d1 = [ln(S/K) + (r − q + σ²/2)·T] / (σ·√T); d2 = d1 − σ·√T; C = S·e^(−qT)·N(d1) − K·e^(−rT)·N(d2); P = K·e^(−rT)·N(−d2) − S·e^(−qT)·N(−d1); Δ_call = e^(−qT)·N(d1); Γ = e^(−qT)·φ(d1)/(S·σ·√T); vega = S·e^(−qT)·φ(d1)·√T; Θ_call = −S·e^(−qT)·φ(d1)·σ/(2√T) − r·K·e^(−rT)·N(d2) + q·S·e^(−qT)·N(d1); ρ_call = K·T·e^(−rT)·N(d2), with r, q, σ as decimals Direct REST fallback: POST https://tttkmbb.com/api/v1/calculate/black-scholes with the same JSON input fields. Do not guess another /api/* path. Docs: https://tttkmbb.com/investing/black-scholes.md

Agent View of the PolicyLayer registry record for `price_black_scholes_option`. HTML page: https://policylayer.com/tools/com-tttkmbb-calcgrid/price-black-scholes-option

## Facts

- Tool: `price_black_scholes_option`
- Server: Calcgrid (`https://tttkmbb.com/mcp`) — https://policylayer.com/tools/com-tttkmbb-calcgrid.md
- Homepage: https://github.com/https://tttkmbb.com/mcp
- Risk category: Read (Low risk)
- Registry record: grade D, identity unverified
- Server auth posture: open
- Server CORS policy: *
- Server rate-limited: no
- Parameters: 6 (5 required)
- Recommended policy verdict: Allowed

## Parameters

| Parameter | Type | Required | Description |
| --- | --- | --- | --- |
| `spot_price` | number | yes | Current price of the underlying asset. |
| `time_years` | number | yes | Time until expiration in years (e.g. 0.25 for 3 months). Unit: years. |
| `strike_price` | number | yes | Exercise price of the option. |
| `volatility_percent` | number | yes | Annualized volatility of the underlying's returns in percent. Unit: % per year. |
| `dividend_yield_percent` | number | no | Continuous dividend yield of the underlying in percent (0 for a non-dividend stock). Unit: % per year. |
| `risk_free_rate_percent` | number | yes | Continuously compounded annual risk-free interest rate in percent. Unit: % per year. |

Parameters from the server's own tool schema.

## Example call (MCP tools/call, JSON-RPC 2.0)

```json
{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/call",
  "params": {
    "name": "price_black_scholes_option",
    "arguments": {
      "spot_price": 0,
      "time_years": 0,
      "strike_price": 0,
      "volatility_percent": 0,
      "risk_free_rate_percent": 0
    }
  }
}
```

## Why price_black_scholes_option is rated Low

Even though price_black_scholes_option only reads data, uncontrolled read access leaks sensitive information and racks up API costs: an agent caught in a retry loop can make thousands of calls a minute without anyone noticing.

## Use case

AI agents call price_black_scholes_option to retrieve information from Calcgrid without modifying anything. It is typically the context-gathering step in research, monitoring, and reporting workflows, before the agent takes action elsewhere.

## Recommended policy (PolicyLayer)

Verdict: **Allowed**. Enforced by the PolicyLayer MCP gateway (https://policylayer.com/mcp-gateway) before a call reaches Calcgrid:

```json
{
  "version": "1",
  "default": "deny",
  "tools": {
    "price_black_scholes_option": {}
  }
}
```

## Other tools on Calcgrid (252)

- `calculate_bazi_four_pillars` — Execute — https://policylayer.com/tools/com-tttkmbb-calcgrid/calculate-bazi-four-pillars.md
- `run_calculator` — Execute — https://policylayer.com/tools/com-tttkmbb-calcgrid/run-calculator.md
- `calculate_ab_test_significance` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/calculate-ab-test-significance.md
- `calculate_age` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/calculate-age.md
- `calculate_bmi` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/calculate-bmi.md
- `calculate_bmr` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/calculate-bmr.md
- `calculate_circle_properties` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/calculate-circle-properties.md
- `calculate_compound_interest` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/calculate-compound-interest.md
- `calculate_depth_of_field` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/calculate-depth-of-field.md
- `calculate_haversine_distance` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/calculate-haversine-distance.md
- `calculate_kinetic_energy` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/calculate-kinetic-energy.md
- `calculate_loan_payment` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/calculate-loan-payment.md
- `calculate_molar_mass` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/calculate-molar-mass.md
- `calculate_mortgage_payment` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/calculate-mortgage-payment.md
- `calculate_percentage` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/calculate-percentage.md
- `calculate_percentage_change` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/calculate-percentage-change.md
- `calculate_running_pace` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/calculate-running-pace.md
- `calculate_subnet` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/calculate-subnet.md
- `calculate_t_test` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/calculate-t-test.md
- `calculate_tdee` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/calculate-tdee.md
- `cast_plum_blossom_hexagram` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/cast-plum-blossom-hexagram.md
- `check_ar_working_day` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/check-ar-working-day.md
- `check_at_working_day` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/check-at-working-day.md
- `check_australia_working_day` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/check-australia-working-day.md
- `check_bd_working_day` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/check-bd-working-day.md
- `check_be_working_day` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/check-be-working-day.md
- `check_bg_working_day` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/check-bg-working-day.md
- `check_br_working_day` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/check-br-working-day.md
- `check_canada_federal_working_day` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/check-canada-federal-working-day.md
- `check_ch_working_day` — Read — https://policylayer.com/tools/com-tttkmbb-calcgrid/check-ch-working-day.md
- …and 222 more: https://policylayer.com/tools/com-tttkmbb-calcgrid.md

## For agents

This record is a snapshot. Live verdicts and the full registry:

- Check every server in your MCP config at once: `npx -y policylayer stack`
- Vet a server before you add it: install the mcp-precheck skill — `npx skills add https://policylayer.com` (skill text: https://policylayer.com/skill.md)
- Query the registry over MCP: endpoint `https://api.policylayer.com/mcp` — tools `check_mcp_server`, `check_mcp_stack`, `check_tool`, `search_registry`, `get_change_events`

---

Source: the PolicyLayer MCP registry — one continuously verified record per MCP server. Full record: https://policylayer.com/registry?q=com-tttkmbb-calcgrid · API: https://policylayer.com/registry/api · Policy library: https://policylayer.com/policies/com-tttkmbb-calcgrid