> ## 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.

# Volatility Smile

> Extract the volatility smile (volatility vs strike) for a specific expiry from a volatility surface. Returns interpolated volatilities for multiple strike points at a single expiry. Essential for analyzing skew, pricing options across strikes, and understanding market expectations of future price distributions. [Tier: PRO, Credits: 5]



## OpenAPI

````yaml api-specs/volatility.json post /quantlib/volatility/surface/smile
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/smile:
    post:
      tags:
        - quantlib-volatility
      summary: Volatility Smile
      description: >-
        Extract the volatility smile (volatility vs strike) for a specific
        expiry from a volatility surface. Returns interpolated volatilities for
        multiple strike points at a single expiry. Essential for analyzing skew,
        pricing options across strikes, and understanding market expectations of
        future price distributions. [Tier: PRO, Credits: 5]
      operationId: surface_smile
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - expiries
                - strikes
                - vol_matrix
                - query_expiry
                - query_strikes
              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 for which to extract the smile
                  example: 0.5
                  minimum: 0
                query_strikes:
                  type: array
                  items:
                    type: number
                  description: Array of strikes at which to evaluate the smile
                  example:
                    - 92
                    - 97
                    - 102
                    - 107
                  minItems: 1
            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_strikes:
                - 92
                - 97
                - 102
                - 107
      responses:
        '200':
          description: Successful Response
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      expiry:
                        type: number
                        description: Query expiry (echo of input)
                        example: 0.5
                      smile:
                        type: array
                        items:
                          type: object
                          properties:
                            strike:
                              type: number
                              description: Strike price
                            volatility:
                              type: number
                              description: Interpolated volatility at this strike
                        description: Array of strike-volatility pairs forming the smile
                        example:
                          - strike: 92
                            volatility: 0.262
                          - strike: 97
                            volatility: 0.244
                          - strike: 102
                            volatility: 0.236
                          - strike: 107
                            volatility: 0.249
              example:
                success: true
                data:
                  expiry: 0.5
                  smile:
                    - strike: 92
                      volatility: 0.262
                    - strike: 97
                      volatility: 0.244
                    - strike: 102
                      volatility: 0.236
                    - strike: 107
                      volatility: 0.249
        '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

````