# GET /api/mcp/data/third-order-greeks/{ticker}

> How fast do SPY's gamma and vega change as spot and vol move?

Returns the third-order Greeks per strike and per contract for one expiration, with a definitions block so a caller can label them.

- **Family:** Options Greeks (https://apexvol.com/developers/options-greeks-api)
- **Plan:** Pro and above. Every call needs `Authorization: Bearer avmcp_<token>`; tokens are issued to paid and trial accounts under Account, then API Access.
- **Units:** Per-share sensitivities for one contract; speed is gamma per dollar of spot, color is gamma per day, vomma is vega per vol point.
- **Basis:** Analytic Black-Scholes derivatives on the chain IV.
- **MCP tools:** `get_third_order_greeks`
- **Background:** https://apexvol.com/learn/options-greeks-cheat-sheet

## Parameters

| Name | In | Default | Range | Meaning |
|---|---|---|---|---|
| `ticker` (required) | path |  | any covered symbol | The underlying, upper case. Use /search to check coverage. |
| `expiration` | query | nearest | YYYY-MM-DD, a listed expiration | Which expiration to use. Defaults to the nearest one. |

## Request

```bash
curl -H "Authorization: Bearer avmcp_YOUR_TOKEN" \
     "https://apexvol.com/api/mcp/data/third-order-greeks/SPY"
```

## Response (captured 2026-09-08)

Real response, lists cut to the rows nearest the money. The envelope is `{"success": true, "data": ...}`.

```json
{
  "success": true,
  "data": {
    "data_status": "LIVE",
    "definitions": {
      "charm": "dDelta/dTime - Delta decay over time",
      "color": "dGamma/dTime - How gamma changes as time passes",
      "speed": "dGamma/dSpot - Rate of change of gamma with spot price",
      "ultima": "dVomma/dVol - Third derivative wrt volatility",
      "vanna": "dDelta/dVol - Delta sensitivity to volatility",
      "vomma": "dVega/dVol - Convexity of vega (volga)",
      "zomma": "dGamma/dVol - Sensitivity of gamma to volatility changes"
    },
    "detailed": [
      {
        "charm": 17.7874,
        "color": -87.5795,
        "iv": 0.0568,
        "speed": -0.0285,
        "strike": 770,
        "type": "C",
        "ultima": -3.5317,
        "vanna": -1.2757,
        "vomma": 0.0677,
        "zomma": -4.129
      },
      {
        "charm": 16.4516,
        "color": -81.4013,
        "iv": 0.0615,
        "speed": -0.0226,
        "strike": 770,
        "type": "P",
        "ultima": -2.5843,
        "vanna": -1.0907,
        "vomma": 0.0535,
        "zomma": -3.552
      },
      {
        "charm": -67.758,
        "color": -65.5505,
        "iv": 0.0556,
        "speed": 0.0641,
        "strike": 771,
        "type": "C",
        "ultima": -18.3207,
        "vanna": 2.8936,
        "vomma": 0.3634,
        "zomma": -3.3136
      }
    ],
    "dte": 0,
    "expiration": "2026-09-08",
    "greeks_by_strike": [
      {
        "charm": 76.9258,
        "color": -30.0987,
        "speed": -0.0772,
        "strike": 769,
        "ultima": -32.2742,
        "vanna": -3.7337,
        "vomma": 0.8049,
        "zomma": -1.2163
      },
      {
        "charm": 17.1195,
        "color": -84.4904,
        "speed": -0.0256,
        "strike": 770,
        "ultima": -3.058,
        "vanna": -1.1832,
        "vomma": 0.0606,
        "zomma": -3.8405
      },
      {
        "charm": -65.3123,
        "color": -64.6529,
        "speed": 0.0567,
        "strike": 771,
        "ultima": -15.6858,
        "vanna": 2.6714,
        "vomma": 0.3219,
        "zomma": -3.1162
      }
    ],
    "stock_price": 770.25,
    "ticker": "SPY"
  }
}
```

## Fields

- `greeks_by_strike[].speed, zomma, color, vomma, ultima, vanna, charm`: Per strike.
- `detailed[]`: Per contract with type and IV.
- `definitions`: One line per Greek.

## Errors

- `401`: no or revoked token
- `429`: Retry-After seconds
- `403`: Pro plan required
- `424`: data feed unavailable, retry
- Full list: https://apexvol.com/developers/errors

## Ask it in an MCP client

- Show third-order Greeks for SPY at the money.
- Where is vomma highest on NVDA?
- How does gamma change with spot on QQQ, strike by strike?

Conventions for units, bases and timestamps: https://apexvol.com/developers/conventions