> ## 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 Jump-Diffusion Option Pricing

> Price European call options using the Merton jump-diffusion model. This model extends Black-Scholes by adding random jumps to account for sudden price movements (earnings announcements, market crashes, etc.). Useful for pricing options on stocks with discontinuous price behavior and understanding jump risk premiums. [Tier: ENTERPRISE, Credits: 10]



## OpenAPI

````yaml api-specs/models.json post /quantlib/models/merton/price
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/price:
    post:
      tags:
        - quantlib-models
      summary: Merton Jump-Diffusion Option Pricing
      description: >-
        Price European call options using the Merton jump-diffusion model. This
        model extends Black-Scholes by adding random jumps to account for sudden
        price movements (earnings announcements, market crashes, etc.). Useful
        for pricing options on stocks with discontinuous price behavior and
        understanding jump risk premiums. [Tier: ENTERPRISE, Credits: 10]
      operationId: merton_price
      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: Strike price
                T:
                  type: number
                  description: Time to maturity in years
                r:
                  type: number
                  description: Risk-free rate (annualized)
                sigma:
                  type: number
                  description: Diffusion volatility (continuous part, annualized)
                lambda_jump:
                  type: number
                  description: >-
                    Jump intensity (average number of jumps per year, e.g., 2 =
                    2 jumps/year)
                mu_jump:
                  type: number
                  description: Mean log-jump size (e.g., -0.1 for average 10% down jumps)
                sigma_jump:
                  type: number
                  description: Jump size volatility (standard deviation of log-jump)
                q:
                  type: number
                  default: 0
                  description: Dividend yield (annualized)
              example:
                S: 100
                K: 105
                T: 1
                r: 0.05
                sigma: 0.2
                lambda_jump: 1.5
                mu_jump: -0.05
                sigma_jump: 0.15
                q: 0.02
      responses:
        '200':
          description: Successfully priced Merton jump-diffusion option
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      merton_call_price:
                        type: number
                        description: Call option price under Merton model
                    example:
                      merton_call_price: 6.42
        '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

````