> ## 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.

# Convert Between Forward and Futures Rates

> Convert between forward rates and futures rates accounting for the convexity adjustment due to daily marking-to-market of futures. Futures contracts are marked to market daily, creating a funding advantage/disadvantage compared to forwards depending on interest rate movements. This leads to a systematic difference between futures and forward rates. Supports both simple and Hull-White models for the adjustment. Essential for pricing Eurodollar futures, Treasury futures, and understanding forward-futures arbitrage. [Tier: STANDARD, Credits: 2]



## OpenAPI

````yaml api-specs/solver.json post /quantlib/solver/finance/forward-futures-conversion
openapi: 3.1.0
info:
  title: FinceptQuantLib API - Solver
  description: >-
    Solver module endpoints for FinceptQuantLib API. The Solver module (Basic
    Tier, 1 credit per request) provides advanced financial solvers including
    bond analytics (yield, duration, convexity), implied volatility
    calculations, spread computations (Z-spread, ASW, OAS), curve bootstrapping,
    interest rate conversions, and model calibration (Vasicek, CIR). Essential
    for fixed income analysis, derivatives pricing, and risk management.
  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-solver
    description: >-
      Advanced financial solvers for bond analytics, implied volatility, spread
      calculations, and model calibration
    x-displayName: Solver
paths:
  /quantlib/solver/finance/forward-futures-conversion:
    post:
      tags:
        - quantlib-solver
      summary: Convert Between Forward and Futures Rates
      description: >-
        Convert between forward rates and futures rates accounting for the
        convexity adjustment due to daily marking-to-market of futures. Futures
        contracts are marked to market daily, creating a funding
        advantage/disadvantage compared to forwards depending on interest rate
        movements. This leads to a systematic difference between futures and
        forward rates. Supports both simple and Hull-White models for the
        adjustment. Essential for pricing Eurodollar futures, Treasury futures,
        and understanding forward-futures arbitrage. [Tier: STANDARD, Credits:
        2]
      operationId: fwd_fut_conv
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - rate
                - volatility
                - t1
                - t2
              properties:
                rate:
                  type: number
                  description: Input rate (forward or futures rate) as a decimal
                  example: 0.03
                volatility:
                  type: number
                  description: Interest rate volatility as a decimal
                  example: 0.01
                t1:
                  type: number
                  description: Time to futures expiry in years
                  example: 1
                t2:
                  type: number
                  description: Time to underlying forward end in years
                  example: 1.25
                direction:
                  type: string
                  description: Conversion direction
                  default: forward_to_futures
                  enum:
                    - forward_to_futures
                    - futures_to_forward
                  example: forward_to_futures
                model:
                  type: string
                  description: Model for convexity adjustment
                  default: simple
                  enum:
                    - simple
                    - hull_white
                  example: simple
                mean_reversion:
                  type: number
                  description: Mean reversion parameter (used in Hull-White model)
                  default: 0.03
                  example: 0.03
            example:
              rate: 0.03
              volatility: 0.01
              t1: 1
              t2: 1.25
              direction: forward_to_futures
              model: simple
              mean_reversion: 0.03
      responses:
        '200':
          description: Successful Response
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      futures_rate:
                        type: number
                        description: The futures rate (if converting from forward)
                        example: 0.030012
                      forward_rate:
                        type: number
                        description: >-
                          The forward rate (if converting from futures or
                          original input)
                        example: 0.03
              example:
                success: true
                data:
                  futures_rate: 0.030012
                  forward_rate: 0.03
        '401':
          $ref: '#/components/responses/UnauthorizedError'
        '402':
          $ref: '#/components/responses/InsufficientTierError'
        '422':
          description: Validation Error
          content:
            application/json:
              schema:
                type: object
                properties:
                  detail:
                    type: array
                    items:
                      type: object
      security:
        - APIKeyHeader: []
components:
  responses:
    UnauthorizedError:
      description: Authentication information is missing or invalid
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Invalid API key
    InsufficientTierError:
      description: API tier insufficient for this endpoint
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Endpoint requires Basic tier or higher
  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

````