> ## 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.

# Implied to Local Volatility Conversion

> Convert implied volatility to local volatility using the Dupire formula. Calculates the instantaneous local volatility at a specific (strike, expiry) point from an implied volatility surface. Uses finite differences to approximate derivatives. Essential for building local volatility surfaces for exotic option pricing and Monte Carlo simulations. [Tier: PRO, Credits: 5]



## OpenAPI

````yaml api-specs/volatility.json post /quantlib/volatility/local-vol/implied-to-local
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/local-vol/implied-to-local:
    post:
      tags:
        - quantlib-volatility
      summary: Implied to Local Volatility Conversion
      description: >-
        Convert implied volatility to local volatility using the Dupire formula.
        Calculates the instantaneous local volatility at a specific (strike,
        expiry) point from an implied volatility surface. Uses finite
        differences to approximate derivatives. Essential for building local
        volatility surfaces for exotic option pricing and Monte Carlo
        simulations. [Tier: PRO, Credits: 5]
      operationId: implied_to_local
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - spot
                - rate
                - strike
                - expiry
                - implied_vol
              properties:
                spot:
                  type: number
                  description: Current spot price of the underlying
                  example: 100
                  minimum: 0
                rate:
                  type: number
                  description: Risk-free interest rate (continuously compounded)
                  example: 0.05
                  minimum: -0.1
                  maximum: 1
                strike:
                  type: number
                  description: Strike price for local vol calculation
                  example: 105
                  minimum: 0
                expiry:
                  type: number
                  description: Time to expiry in years
                  example: 1
                  minimum: 0
                implied_vol:
                  type: number
                  description: >-
                    Implied volatility at (strike, expiry). For full surface
                    conversion, use a volatility surface function
                  example: 0.25
                  minimum: 0
                  maximum: 5
                dk:
                  type: number
                  description: >-
                    Strike increment for finite difference (as fraction of
                    strike)
                  default: 0.01
                  example: 0.01
                  minimum: 0.0001
                  maximum: 0.1
                dt:
                  type: number
                  description: Time increment for finite difference (in years)
                  default: 0.01
                  example: 0.01
                  minimum: 0.0001
                  maximum: 0.1
            example:
              spot: 100
              rate: 0.05
              strike: 105
              expiry: 1
              implied_vol: 0.25
              dk: 0.01
              dt: 0.01
      responses:
        '200':
          description: Successful Response
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      local_vol:
                        type: number
                        description: >-
                          Local volatility at (strike, expiry) computed via
                          Dupire formula
                        example: 0.2465
                      implied_vol:
                        type: number
                        description: Implied volatility (echo of input)
                        example: 0.25
                      spot:
                        type: number
                        description: Spot price (echo of input)
                        example: 100
                      strike:
                        type: number
                        description: Strike price (echo of input)
                        example: 105
                      expiry:
                        type: number
                        description: Expiry time (echo of input)
                        example: 1
              example:
                success: true
                data:
                  local_vol: 0.2465
                  implied_vol: 0.25
                  spot: 100
                  strike: 105
                  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

````