> ## 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.

# Hull-White Model Calibration

> Calibrate a Hull-White short rate model to match market yield curve data. The Hull-White model extends Vasicek by fitting an initial term structure, making it ideal for pricing derivatives consistently with observed market rates. Use this endpoint to calibrate the model parameters and generate fitted bond prices for validation. [Tier: ENTERPRISE, Credits: 10]



## OpenAPI

````yaml api-specs/models.json post /quantlib/models/hull-white/calibrate
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/hull-white/calibrate:
    post:
      tags:
        - quantlib-models
      summary: Hull-White Model Calibration
      description: >-
        Calibrate a Hull-White short rate model to match market yield curve
        data. The Hull-White model extends Vasicek by fitting an initial term
        structure, making it ideal for pricing derivatives consistently with
        observed market rates. Use this endpoint to calibrate the model
        parameters and generate fitted bond prices for validation. [Tier:
        ENTERPRISE, Credits: 10]
      operationId: hw_calibrate
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - market_tenors
                - market_rates
              properties:
                kappa:
                  type: number
                  default: 0.1
                  description: Mean reversion speed parameter (fixed during calibration)
                sigma:
                  type: number
                  default: 0.01
                  description: Volatility parameter (fixed during calibration)
                r0:
                  type: number
                  default: 0.03
                  description: Initial short rate
                market_tenors:
                  type: array
                  items:
                    type: number
                  description: >-
                    Array of market rate tenors in years (e.g., [0.5, 1, 2, 5,
                    10])
                market_rates:
                  type: array
                  items:
                    type: number
                  description: >-
                    Corresponding market rates (yields) for each tenor,
                    annualized
              example:
                kappa: 0.15
                sigma: 0.012
                r0: 0.025
                market_tenors:
                  - 0.5
                  - 1
                  - 2
                  - 5
                  - 10
                market_rates:
                  - 0.0275
                  - 0.03
                  - 0.0345
                  - 0.04
                  - 0.045
      responses:
        '200':
          description: Successfully calibrated Hull-White model
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      model:
                        type: string
                        example: hull_white
                      calibrated_bonds:
                        type: array
                        items:
                          type: object
                          properties:
                            maturity:
                              type: number
                              description: Bond maturity in years
                            bond_price:
                              type: number
                              description: Calibrated bond price from the Hull-White model
                    example:
                      model: hull_white
                      calibrated_bonds:
                        - maturity: 0.5
                          bond_price: 98.64
                        - maturity: 1
                          bond_price: 97.04
                        - maturity: 2
                          bond_price: 93.32
                        - maturity: 5
                          bond_price: 81.87
                        - maturity: 10
                          bond_price: 64.07
        '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

````