> ## 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.

# Shifted Lognormal Option Price

> Price options using the shifted lognormal model, which applies a shift parameter to handle negative or very low rates while maintaining lognormal distribution properties.

**Model:** ln(F + shift) ~ Normal(μ, σ²t)

**Use Cases:**
- Price options when forwards/rates can be negative
- Bridge between lognormal and normal models
- Model interest rate options in low/negative rate environments
- Calibrate to market with better fit than pure lognormal or normal

**Shift Parameter:** Typically set to make F + shift > 0. Common choices: shift = 0.02-0.05 for interest rates.

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



## OpenAPI

````yaml api-specs/pricing.json post /quantlib/pricing/bachelier/shifted-lognormal
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/bachelier/shifted-lognormal:
    post:
      tags:
        - quantlib-pricing
      summary: Shifted Lognormal Option Price
      description: >-
        Price options using the shifted lognormal model, which applies a shift
        parameter to handle negative or very low rates while maintaining
        lognormal distribution properties.


        **Model:** ln(F + shift) ~ Normal(μ, σ²t)


        **Use Cases:**

        - Price options when forwards/rates can be negative

        - Bridge between lognormal and normal models

        - Model interest rate options in low/negative rate environments

        - Calibrate to market with better fit than pure lognormal or normal


        **Shift Parameter:** Typically set to make F + shift > 0. Common
        choices: shift = 0.02-0.05 for interest rates.


        **Tier:** Standard (2 credits/request) [Tier: PRO, Credits: 5]
      operationId: shifted_lognormal
      requestBody:
        required: true
        content:
          application/json:
            schema:
              $ref: '#/components/schemas/ShiftedLognormalRequest'
            example:
              forward: 0.02
              strike: 0.025
              risk_free_rate: 0.01
              volatility: 0.5
              time_to_maturity: 2
              shift: 0.03
              option_type: call
      responses:
        '200':
          description: Successful calculation
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      price:
                        type: number
                        description: Calculated option price
                        example: 0.0089
                      shift:
                        type: number
                        description: Shift parameter used
                        example: 0.03
                      option_type:
                        type: string
                        example: call
        '401':
          $ref: '#/components/responses/UnauthorizedError'
        '402':
          $ref: '#/components/responses/InsufficientCreditsError'
        '422':
          $ref: '#/components/responses/ValidationError'
components:
  schemas:
    ShiftedLognormalRequest:
      type: object
      required:
        - forward
        - strike
        - risk_free_rate
        - volatility
        - time_to_maturity
      properties:
        forward:
          type: number
          description: Forward price of the underlying asset
          example: 102
        strike:
          type: number
          description: Strike price of the option
          example: 105
        risk_free_rate:
          type: number
          description: Risk-free interest rate (annualized, decimal format)
          example: 0.05
        volatility:
          type: number
          description: Annualized volatility (decimal format)
          example: 0.25
        time_to_maturity:
          type: number
          description: Time to expiration in years
          example: 1
        shift:
          type: number
          description: Shift parameter for the shifted lognormal model
          example: 0.03
          default: 0
        option_type:
          type: string
          enum:
            - call
            - put
          description: Type of option
          example: call
          default: call
  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

````