> ## 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.

# Merton Model FFT Pricing

> Price options using Fast Fourier Transform (FFT) methods for the Merton jump-diffusion model. FFT pricing is highly efficient for computing option prices across multiple strikes simultaneously, making it ideal for constructing option chains, implied volatility surfaces, and risk analysis. Returns prices for a range of strikes in a single computation. [Tier: ENTERPRISE, Credits: 10]



## OpenAPI

````yaml api-specs/models.json post /quantlib/models/merton/fft
openapi: 3.1.0
info:
  title: FinceptQuantLib API - Models
  description: >-
    Advanced financial modeling module for short rate models, stochastic
    volatility, jump-diffusion processes, and local volatility models. Pro Tier
    required (5 credits per request).
  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-models
    description: >-
      Advanced financial modeling including short rate models, stochastic
      volatility, jump-diffusion, and local volatility models
    x-displayName: Models
paths:
  /quantlib/models/merton/fft:
    post:
      tags:
        - quantlib-models
      summary: Merton Model FFT Pricing
      description: >-
        Price options using Fast Fourier Transform (FFT) methods for the Merton
        jump-diffusion model. FFT pricing is highly efficient for computing
        option prices across multiple strikes simultaneously, making it ideal
        for constructing option chains, implied volatility surfaces, and risk
        analysis. Returns prices for a range of strikes in a single computation.
        [Tier: ENTERPRISE, Credits: 10]
      operationId: merton_fft
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - S
                - K
                - T
                - r
                - sigma
                - lambda_jump
                - mu_jump
                - sigma_jump
              properties:
                S:
                  type: number
                  description: Current stock price
                K:
                  type: number
                  description: >-
                    Reference strike price (FFT computes prices for a range
                    around this)
                T:
                  type: number
                  description: Time to maturity in years
                r:
                  type: number
                  description: Risk-free rate
                sigma:
                  type: number
                  description: Diffusion volatility
                lambda_jump:
                  type: number
                  description: Jump intensity
                mu_jump:
                  type: number
                  description: Mean log-jump size
                sigma_jump:
                  type: number
                  description: Jump size volatility
                q:
                  type: number
                  default: 0
                  description: Dividend yield
              example:
                S: 100
                K: 100
                T: 0.5
                r: 0.05
                sigma: 0.25
                lambda_jump: 2
                mu_jump: -0.08
                sigma_jump: 0.12
                q: 0
      responses:
        '200':
          description: Successfully computed FFT option prices
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      strikes:
                        type: array
                        items:
                          type: number
                        description: Array of strike prices computed by FFT
                      call_prices:
                        type: array
                        items:
                          type: number
                        description: Corresponding call option prices
                      put_prices:
                        type: array
                        items:
                          type: number
                        description: Corresponding put option prices
                    example:
                      strikes:
                        - 85
                        - 90
                        - 95
                        - 100
                        - 105
                        - 110
                        - 115
                      call_prices:
                        - 16.23
                        - 12.45
                        - 9.12
                        - 6.42
                        - 4.35
                        - 2.87
                        - 1.84
                      put_prices:
                        - 0.87
                        - 1.98
                        - 3.64
                        - 5.87
                        - 8.72
                        - 12.15
                        - 16.08
        '401':
          $ref: '#/components/responses/UnauthorizedError'
        '402':
          $ref: '#/components/responses/InsufficientCreditsError'
        '422':
          $ref: '#/components/responses/ValidationError'
components:
  responses:
    UnauthorizedError:
      description: Authentication information is missing or invalid
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Invalid API key
    InsufficientCreditsError:
      description: Insufficient credits to complete the request
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: >-
                  Insufficient credits. This endpoint requires 5 credits.
                  Current balance: 2 credits.
    ValidationError:
      description: Request validation failed
      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
                  - kappa
                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

````