> ## 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.

# Total Variance from Surface

> Query total variance (volatility^2 * time) from a volatility surface at a specific expiry and strike. Total variance is fundamental for option pricing models and ensures proper scaling of volatility across different time horizons. Used in variance swaps, volatility derivatives, and model calibration. [Tier: PRO, Credits: 5]



## OpenAPI

````yaml api-specs/volatility.json post /quantlib/volatility/surface/total-variance
openapi: 3.1.0
info:
  title: FinceptQuantLib API - Volatility
  description: >-
    Volatility module endpoints for FinceptQuantLib API. Standard Tier module (2
    credits per request) providing comprehensive volatility surface modeling,
    SABR model calibration and analytics, and local volatility calculations for
    derivatives pricing and risk management.
  version: 3.0.0
  contact:
    name: Fincept API Support
    url: https://fincept.in
servers:
  - url: https://api.fincept.in
    description: Fincept API Production Server
security:
  - APIKeyHeader: []
tags:
  - name: quantlib-volatility
    description: >-
      Volatility surface modeling, SABR calibration, and local volatility
      calculations
    x-displayName: Volatility
paths:
  /quantlib/volatility/surface/total-variance:
    post:
      tags:
        - quantlib-volatility
      summary: Total Variance from Surface
      description: >-
        Query total variance (volatility^2 * time) from a volatility surface at
        a specific expiry and strike. Total variance is fundamental for option
        pricing models and ensures proper scaling of volatility across different
        time horizons. Used in variance swaps, volatility derivatives, and model
        calibration. [Tier: PRO, Credits: 5]
      operationId: surface_total_variance
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - expiries
                - strikes
                - vol_matrix
                - query_expiry
                - query_strike
              properties:
                expiries:
                  type: array
                  items:
                    type: number
                  description: Array of expiry times in years
                  example:
                    - 0.25
                    - 0.5
                    - 1
                  minItems: 2
                strikes:
                  type: array
                  items:
                    type: number
                  description: Array of strike prices
                  example:
                    - 90
                    - 95
                    - 100
                    - 105
                    - 110
                  minItems: 2
                vol_matrix:
                  type: array
                  items:
                    type: array
                    items:
                      type: number
                  description: 2D volatility matrix [expiry_index][strike_index]
                  example:
                    - - 0.28
                      - 0.26
                      - 0.24
                      - 0.25
                      - 0.27
                    - - 0.27
                      - 0.25
                      - 0.23
                      - 0.24
                      - 0.26
                    - - 0.26
                      - 0.24
                      - 0.22
                      - 0.23
                      - 0.25
                query_expiry:
                  type: number
                  description: Expiry time in years for the query
                  example: 0.5
                  minimum: 0
                query_strike:
                  type: number
                  description: Strike price for the query
                  example: 100
                  minimum: 0
            example:
              expiries:
                - 0.25
                - 0.5
                - 1
              strikes:
                - 90
                - 95
                - 100
                - 105
                - 110
              vol_matrix:
                - - 0.28
                  - 0.26
                  - 0.24
                  - 0.25
                  - 0.27
                - - 0.27
                  - 0.25
                  - 0.23
                  - 0.24
                  - 0.26
                - - 0.26
                  - 0.24
                  - 0.22
                  - 0.23
                  - 0.25
              query_expiry: 0.5
              query_strike: 100
      responses:
        '200':
          description: Successful Response
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      total_variance:
                        type: number
                        description: Total variance (sigma^2 * T)
                        example: 0.026245
                      expiry:
                        type: number
                        description: Query expiry (echo of input)
                        example: 0.5
                      strike:
                        type: number
                        description: Query strike (echo of input)
                        example: 100
              example:
                success: true
                data:
                  total_variance: 0.026245
                  expiry: 0.5
                  strike: 100
        '401':
          $ref: '#/components/responses/UnauthorizedError'
        '402':
          $ref: '#/components/responses/InsufficientTierError'
        '422':
          $ref: '#/components/responses/ValidationError'
      security:
        - APIKeyHeader: []
components:
  responses:
    UnauthorizedError:
      description: Authentication information is missing or invalid
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Invalid API key
    InsufficientTierError:
      description: API tier insufficient for this endpoint
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Endpoint requires Standard tier or higher
    ValidationError:
      description: 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
          example:
            detail:
              - loc:
                  - body
                  - volatility
                msg: field required
                type: value_error.missing
  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

````