> ## 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.

# Black76 Caplet Price

> Price an interest rate caplet using the Black76 model. A caplet is a call option on an interest rate that pays off when the reference rate exceeds the strike rate.

**Payoff:** max(L - K, 0) × τ × N × DF

Where:
- L = realized LIBOR/forward rate
- K = strike rate
- τ = accrual period (t_end - t_start)
- N = notional
- DF = discount factor

**Use Cases:**
- Price interest rate caps (sum of caplets)
- Hedge floating rate exposures
- Value borrower's protection against rate increases
- Structure interest rate derivatives

**Tier:** Standard (2 credits/request) [Tier: PRO, Credits: 5]



## OpenAPI

````yaml api-specs/pricing.json post /quantlib/pricing/black76/caplet
openapi: 3.1.0
info:
  title: FinceptQuantLib API - Pricing Module
  description: >-
    Advanced options pricing models including Black-Scholes, Black76, Bachelier,
    Kirk spread options, and binomial trees. Standard Tier access required (2
    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-pricing
    description: Advanced options pricing models and Greeks calculation
    x-displayName: Pricing
paths:
  /quantlib/pricing/black76/caplet:
    post:
      tags:
        - quantlib-pricing
      summary: Black76 Caplet Price
      description: >-
        Price an interest rate caplet using the Black76 model. A caplet is a
        call option on an interest rate that pays off when the reference rate
        exceeds the strike rate.


        **Payoff:** max(L - K, 0) × τ × N × DF


        Where:

        - L = realized LIBOR/forward rate

        - K = strike rate

        - τ = accrual period (t_end - t_start)

        - N = notional

        - DF = discount factor


        **Use Cases:**

        - Price interest rate caps (sum of caplets)

        - Hedge floating rate exposures

        - Value borrower's protection against rate increases

        - Structure interest rate derivatives


        **Tier:** Standard (2 credits/request) [Tier: PRO, Credits: 5]
      operationId: black76_caplet
      requestBody:
        required: true
        content:
          application/json:
            schema:
              $ref: '#/components/schemas/CapFloorletRequest'
            example:
              forward_rate: 0.03
              strike: 0.035
              discount_factor: 0.95
              volatility: 0.2
              t_start: 1
              t_end: 1.25
              notional: 1000000
      responses:
        '200':
          description: Successful calculation
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      caplet_price:
                        type: number
                        description: Caplet price
                        example: 234.56
        '401':
          $ref: '#/components/responses/UnauthorizedError'
        '402':
          $ref: '#/components/responses/InsufficientCreditsError'
        '422':
          $ref: '#/components/responses/ValidationError'
components:
  schemas:
    CapFloorletRequest:
      type: object
      required:
        - forward_rate
        - strike
        - discount_factor
        - volatility
        - t_start
        - t_end
      properties:
        forward_rate:
          type: number
          description: Forward interest rate for the period (decimal format)
          example: 0.03
        strike:
          type: number
          description: Strike rate of the caplet/floorlet (decimal format)
          example: 0.035
        discount_factor:
          type: number
          description: Discount factor to present value
          example: 0.95
        volatility:
          type: number
          description: Annualized volatility of the forward rate (decimal format)
          example: 0.2
        t_start:
          type: number
          description: Start time of the accrual period in years
          example: 1
        t_end:
          type: number
          description: End time of the accrual period in years
          example: 1.25
        notional:
          type: number
          description: Notional amount
          example: 1000000
          default: 1
  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 API credits for this request
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: >-
                  Insufficient credits. This endpoint costs 2 credits per
                  request.
    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
  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

````