> ## 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.

# SABR Volatility Smile

> Generate a complete SABR volatility smile across multiple strikes for a given expiry. Returns the volatility smile curve along with key smile characteristics: ATM volatility, skew (first derivative), and curvature (second derivative). Essential for understanding market expectations and pricing options across the strike spectrum. [Tier: PRO, Credits: 5]



## OpenAPI

````yaml api-specs/volatility.json post /quantlib/volatility/sabr/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/sabr/smile:
    post:
      tags:
        - quantlib-volatility
      summary: SABR Volatility Smile
      description: >-
        Generate a complete SABR volatility smile across multiple strikes for a
        given expiry. Returns the volatility smile curve along with key smile
        characteristics: ATM volatility, skew (first derivative), and curvature
        (second derivative). Essential for understanding market expectations and
        pricing options across the strike spectrum. [Tier: PRO, Credits: 5]
      operationId: sabr_smile
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - forward
                - expiry
                - alpha
                - beta
                - rho
                - nu
                - strikes
              properties:
                forward:
                  type: number
                  description: Forward price of the underlying
                  example: 100
                  minimum: 0
                expiry:
                  type: number
                  description: Time to expiry in years
                  example: 1
                  minimum: 0
                alpha:
                  type: number
                  description: SABR alpha parameter (ATM volatility level)
                  example: 0.25
                  minimum: 0
                beta:
                  type: number
                  description: SABR beta parameter (backbone exponent)
                  example: 0.5
                  minimum: 0
                  maximum: 1
                rho:
                  type: number
                  description: SABR rho parameter (skew control)
                  example: -0.2
                  minimum: -1
                  maximum: 1
                nu:
                  type: number
                  description: SABR nu parameter (smile curvature)
                  example: 0.3
                  minimum: 0
                strikes:
                  type: array
                  items:
                    type: number
                  description: Array of strike prices for smile evaluation
                  example:
                    - 90
                    - 95
                    - 100
                    - 105
                    - 110
                  minItems: 2
            example:
              forward: 100
              expiry: 1
              alpha: 0.25
              beta: 0.5
              rho: -0.2
              nu: 0.3
              strikes:
                - 90
                - 95
                - 100
                - 105
                - 110
      responses:
        '200':
          description: Successful Response
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      forward:
                        type: number
                        description: Forward price (echo of input)
                        example: 100
                      expiry:
                        type: number
                        description: Expiry time (echo of input)
                        example: 1
                      atm_vol:
                        type: number
                        description: At-the-money volatility
                        example: 0.25
                      skew:
                        type: number
                        description: Volatility skew (d(vol)/d(strike) at ATM)
                        example: -0.0015
                      curvature:
                        type: number
                        description: Smile curvature (d^2(vol)/d(strike)^2 at ATM)
                        example: 0.00008
                      smile:
                        type: array
                        items:
                          type: object
                          properties:
                            strike:
                              type: number
                              description: Strike price
                            implied_vol:
                              type: number
                              description: SABR implied volatility at this strike
                        description: Array of strike-volatility pairs
                        example:
                          - strike: 90
                            implied_vol: 0.268
                          - strike: 95
                            implied_vol: 0.257
                          - strike: 100
                            implied_vol: 0.25
                          - strike: 105
                            implied_vol: 0.248
                          - strike: 110
                            implied_vol: 0.251
              example:
                success: true
                data:
                  forward: 100
                  expiry: 1
                  atm_vol: 0.25
                  skew: -0.0015
                  curvature: 0.00008
                  smile:
                    - strike: 90
                      implied_vol: 0.268
                    - strike: 95
                      implied_vol: 0.257
                    - strike: 100
                      implied_vol: 0.25
                    - strike: 105
                      implied_vol: 0.248
                    - strike: 110
                      implied_vol: 0.251
        '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

````