> ## Documentation Index
> Fetch the complete documentation index at: https://docs.fincept.in/llms.txt
> Use this file to discover all available pages before exploring further.

# Calculate Cross-Gamma

> Computes mixed second-order sensitivities showing how delta changes with respect to multiple risk factors simultaneously. Important for managing complex derivatives with exposure to multiple underlyings or risk factors. Used in correlation trading and multi-asset option books. [Tier: PRO, Credits: 5]



## OpenAPI

````yaml api-specs/risk.json post /quantlib/risk/sensitivities/cross-gamma
openapi: 3.1.0
info:
  title: FinceptQuantLib API - Risk Module
  description: >-
    Professional-grade risk management endpoints including Value at Risk (VaR),
    stress testing, copulas, extreme value theory (EVT), XVA calculations,
    sensitivities, and portfolio hedging. Part of the Pro Tier (5 credits per
    request).
  version: 3.0.0
  contact:
    name: Fincept API Support
    url: https://fincept.in
    email: support@fincept.in
servers:
  - url: https://api.fincept.in
    description: Fincept API Production Server
security:
  - APIKeyHeader: []
tags:
  - name: quantlib-risk
    description: Risk Management Module - Pro Tier (5 credits/request)
    x-displayName: Risk
paths:
  /quantlib/risk/sensitivities/cross-gamma:
    post:
      tags:
        - quantlib-risk
      summary: Calculate Cross-Gamma
      description: >-
        Computes mixed second-order sensitivities showing how delta changes with
        respect to multiple risk factors simultaneously. Important for managing
        complex derivatives with exposure to multiple underlyings or risk
        factors. Used in correlation trading and multi-asset option books.
        [Tier: PRO, Credits: 5]
      operationId: cross_gamma
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              properties:
                S:
                  type: number
                  description: Current underlying price
                  example: 100
                  default: 100
                K:
                  type: number
                  description: Strike price
                  example: 100
                  default: 100
                T:
                  type: number
                  description: Time to expiration in years
                  example: 1
                  default: 1
                r:
                  type: number
                  description: Risk-free rate
                  example: 0.05
                  default: 0.05
                sigma:
                  type: number
                  description: Volatility
                  example: 0.2
                  default: 0.2
                bump:
                  type: number
                  description: Bump size for finite difference calculation
                  example: 0.01
                  default: 0.01
            example:
              S: 105
              K: 100
              T: 0.75
              r: 0.045
              sigma: 0.22
              bump: 0.01
      responses:
        '200':
          description: Cross-gamma calculation
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      cross_gamma:
                        type: number
                        description: Cross-gamma value
                        example: 0.0234
              example:
                success: true
                data:
                  cross_gamma: 0.0234
        '401':
          $ref: '#/components/responses/UnauthorizedError'
        '402':
          $ref: '#/components/responses/InsufficientCreditsError'
        '422':
          $ref: '#/components/responses/ValidationError'
components:
  responses:
    UnauthorizedError:
      description: Authentication information is missing or invalid
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Invalid API key
    InsufficientCreditsError:
      description: Insufficient API credits for this request
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Insufficient credits. This endpoint requires 5 credits.
    ValidationError:
      description: Request validation error
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: array
                items:
                  type: object
                  properties:
                    loc:
                      type: array
                      items:
                        type: string
                    msg:
                      type: string
                    type:
                      type: string
  securitySchemes:
    APIKeyHeader:
      type: apiKey
      in: header
      name: X-API-Key
      description: >-
        API key for authentication. Get your key at
        https://api.fincept.in/auth/register

````