> ## 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.

# Variance Gamma Option Pricing

> Price European call options using the Variance Gamma (VG) model. The VG model is a pure jump process (no continuous diffusion) that effectively captures the leptokurtic (fat-tailed) and skewed nature of asset returns. It's computationally efficient and provides excellent fits to market option prices, making it popular for equity and FX derivatives. [Tier: ENTERPRISE, Credits: 10]



## OpenAPI

````yaml api-specs/models.json post /quantlib/models/variance-gamma/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/variance-gamma/price:
    post:
      tags:
        - quantlib-models
      summary: Variance Gamma Option Pricing
      description: >-
        Price European call options using the Variance Gamma (VG) model. The VG
        model is a pure jump process (no continuous diffusion) that effectively
        captures the leptokurtic (fat-tailed) and skewed nature of asset
        returns. It's computationally efficient and provides excellent fits to
        market option prices, making it popular for equity and FX derivatives.
        [Tier: ENTERPRISE, Credits: 10]
      operationId: vg_price
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - S
                - K
                - T
                - r
                - sigma
                - theta_vg
                - nu
              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: VG volatility parameter (controls overall volatility level)
                theta_vg:
                  type: number
                  description: >-
                    VG drift/skewness parameter. Negative = left skew (typical
                    for equities). Typical: -0.2 to 0
                nu:
                  type: number
                  description: >-
                    VG kurtosis parameter (controls tail heaviness). Higher =
                    fatter tails. Typical: 0.1-0.5
                q:
                  type: number
                  default: 0
                  description: Dividend yield
              example:
                S: 100
                K: 100
                T: 1
                r: 0.05
                sigma: 0.22
                theta_vg: -0.15
                nu: 0.25
                q: 0
      responses:
        '200':
          description: Successfully priced Variance Gamma option
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      vg_call_price:
                        type: number
                        description: Call option price under Variance Gamma model
                    example:
                      vg_call_price: 8.73
        '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

````