> ## 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 Implied Volatility

> Calculate implied volatility using the SABR (Stochastic Alpha Beta Rho) model. SABR is the industry standard for modeling volatility smiles in interest rate and FX markets. Returns the Black-equivalent implied volatility for a given strike, forward, and SABR parameters (alpha, beta, rho, nu). [Tier: PRO, Credits: 5]



## OpenAPI

````yaml api-specs/volatility.json post /quantlib/volatility/sabr/implied-vol
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/implied-vol:
    post:
      tags:
        - quantlib-volatility
      summary: SABR Implied Volatility
      description: >-
        Calculate implied volatility using the SABR (Stochastic Alpha Beta Rho)
        model. SABR is the industry standard for modeling volatility smiles in
        interest rate and FX markets. Returns the Black-equivalent implied
        volatility for a given strike, forward, and SABR parameters (alpha,
        beta, rho, nu). [Tier: PRO, Credits: 5]
      operationId: sabr_implied_vol
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - forward
                - strike
                - expiry
                - alpha
                - beta
                - rho
                - nu
              properties:
                forward:
                  type: number
                  description: Forward price of the underlying
                  example: 100
                  minimum: 0
                strike:
                  type: number
                  description: Option strike price
                  example: 102
                  minimum: 0
                expiry:
                  type: number
                  description: Time to expiry in years
                  example: 1
                  minimum: 0
                alpha:
                  type: number
                  description: SABR alpha parameter (overall volatility level)
                  example: 0.25
                  minimum: 0
                beta:
                  type: number
                  description: >-
                    SABR beta parameter (0=normal, 1=lognormal, 0.5=CIR).
                    Controls backbone shape
                  example: 0.5
                  minimum: 0
                  maximum: 1
                rho:
                  type: number
                  description: >-
                    SABR rho parameter (correlation between forward and
                    volatility). Controls skew
                  example: -0.2
                  minimum: -1
                  maximum: 1
                nu:
                  type: number
                  description: >-
                    SABR nu parameter (volatility of volatility). Controls smile
                    curvature
                  example: 0.3
                  minimum: 0
            example:
              forward: 100
              strike: 102
              expiry: 1
              alpha: 0.25
              beta: 0.5
              rho: -0.2
              nu: 0.3
      responses:
        '200':
          description: Successful Response
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      implied_vol:
                        type: number
                        description: Black-equivalent implied volatility from SABR
                        example: 0.2423
                      forward:
                        type: number
                        description: Forward price (echo of input)
                        example: 100
                      strike:
                        type: number
                        description: Strike price (echo of input)
                        example: 102
                      expiry:
                        type: number
                        description: Expiry time (echo of input)
                        example: 1
              example:
                success: true
                data:
                  implied_vol: 0.2423
                  forward: 100
                  strike: 102
                  expiry: 1
        '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

````