> ## 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.

# Kou Double Exponential Jump Model

> Price European call options using the Kou double exponential jump-diffusion model. Unlike Merton's model with normal jumps, Kou uses asymmetric exponential distributions for jumps, better capturing the empirical fat tails and skewness in equity returns. Upward and downward jumps have different decay rates, making it ideal for modeling leverage effects and crash risk. [Tier: ENTERPRISE, Credits: 10]



## OpenAPI

````yaml api-specs/models.json post /quantlib/models/kou/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/kou/price:
    post:
      tags:
        - quantlib-models
      summary: Kou Double Exponential Jump Model
      description: >-
        Price European call options using the Kou double exponential
        jump-diffusion model. Unlike Merton's model with normal jumps, Kou uses
        asymmetric exponential distributions for jumps, better capturing the
        empirical fat tails and skewness in equity returns. Upward and downward
        jumps have different decay rates, making it ideal for modeling leverage
        effects and crash risk. [Tier: ENTERPRISE, Credits: 10]
      operationId: kou_price
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - S
                - K
                - T
                - r
                - sigma
                - lambda_jump
                - p
                - eta1
                - eta2
              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
                sigma:
                  type: number
                  description: Diffusion volatility
                lambda_jump:
                  type: number
                  description: Jump intensity (average jumps per year)
                p:
                  type: number
                  description: >-
                    Probability of upward jump (0 < p < 1). Complement (1-p) is
                    downward jump probability
                eta1:
                  type: number
                  description: >-
                    Upward jump mean (decay rate of positive exponential).
                    Typical: 5-30
                eta2:
                  type: number
                  description: >-
                    Downward jump mean (decay rate of negative exponential).
                    Typical: 5-30
                q:
                  type: number
                  default: 0
                  description: Dividend yield
              example:
                S: 100
                K: 105
                T: 0.75
                r: 0.05
                sigma: 0.18
                lambda_jump: 3
                p: 0.4
                eta1: 10
                eta2: 15
                q: 0
      responses:
        '200':
          description: Successfully priced Kou model option
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      kou_call_price:
                        type: number
                        description: Call option price under Kou double exponential model
                    example:
                      kou_call_price: 5.18
        '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

````