> ## 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.

# Heston Model Option Pricing (Analytical)

> Price European options using the Heston stochastic volatility model with analytical formulas. The Heston model captures volatility smile/skew effects better than Black-Scholes by allowing volatility to be stochastic. Perfect for pricing equity options, volatility derivatives, and understanding implied volatility surfaces. Includes Feller condition check for parameter validity. [Tier: ENTERPRISE, Credits: 10]



## OpenAPI

````yaml api-specs/models.json post /quantlib/models/heston/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/heston/price:
    post:
      tags:
        - quantlib-models
      summary: Heston Model Option Pricing (Analytical)
      description: >-
        Price European options using the Heston stochastic volatility model with
        analytical formulas. The Heston model captures volatility smile/skew
        effects better than Black-Scholes by allowing volatility to be
        stochastic. Perfect for pricing equity options, volatility derivatives,
        and understanding implied volatility surfaces. Includes Feller condition
        check for parameter validity. [Tier: ENTERPRISE, Credits: 10]
      operationId: heston_price
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - S0
                - v0
                - r
                - kappa
                - theta
                - sigma_v
                - rho
                - strike
                - T
              properties:
                S0:
                  type: number
                  description: Current stock/asset price (e.g., 100 for $100 stock)
                v0:
                  type: number
                  description: >-
                    Initial variance (volatility squared). For 20% vol, use 0.04
                    (0.20^2)
                r:
                  type: number
                  description: Risk-free rate (annualized, e.g., 0.05 for 5%)
                kappa:
                  type: number
                  description: >-
                    Mean reversion speed of variance. Higher = faster reversion.
                    Typical: 1-5
                theta:
                  type: number
                  description: >-
                    Long-term variance level. This is the variance towards which
                    v reverts
                sigma_v:
                  type: number
                  description: >-
                    Volatility of variance (vol-of-vol). Controls variance
                    randomness. Typical: 0.1-0.5
                rho:
                  type: number
                  description: >-
                    Correlation between stock and variance processes. Negative =
                    leverage effect. Range: -1 to 1
                strike:
                  type: number
                  description: Option strike price
                T:
                  type: number
                  description: Time to maturity in years (e.g., 0.25 for 3 months)
                option_type:
                  type: string
                  enum:
                    - call
                    - put
                  default: call
                  description: 'Option type: call or put'
              example:
                S0: 100
                v0: 0.04
                r: 0.05
                kappa: 2
                theta: 0.04
                sigma_v: 0.3
                rho: -0.7
                strike: 105
                T: 0.5
                option_type: call
      responses:
        '200':
          description: Successfully priced Heston option
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      price:
                        type: number
                        description: >-
                          Option price calculated using Heston analytical
                          formula
                      option_type:
                        type: string
                        example: call
                      feller_condition:
                        type: boolean
                        description: >-
                          True if 2*kappa*theta > sigma_v^2 (ensures variance
                          stays positive)
                    example:
                      price: 4.87
                      option_type: call
                      feller_condition: true
        '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

````