Black-Scholes Calculator

A modern, full-featured Black-Scholes options pricing calculator built with Next.js, React, TypeScript, and TailwindCSS.

Features

Core Functionality

• Option Price Calculation: Calculate European call and put option prices using the Black-Scholes-Merton model
• Greeks Calculation: Compute all major Greeks (Delta, Gamma, Theta, Vega, Rho)
• Implied Volatility: Calculate implied volatility from market option prices using Newton-Raphson method
• Calculation History: View and reload up to 10 most recent calculations

User Interface

• Clean, modern interface with Shadcn UI components
• Responsive design that works on desktop, tablet, and mobile
• Dark mode support
• Real-time form validation with helpful error messages
• Interactive history with one-click reload of previous calculations

Tech Stack

• Framework: Next.js 16 with App Router
• Language: TypeScript
• Styling: TailwindCSS v4
• Components: Shadcn UI
• Testing: Jest + React Testing Library
• Storage: Browser LocalStorage API

Getting Started

Prerequisites

• Node.js 18 or later
• npm or yarn

Installation

1. Clone the repository:

git clone <repository-url>
cd bs-calculator

2. Install dependencies:

cd frontend
npm install

Development

Run the development server:

npm run dev

Open http://localhost:3000 in your browser.

Building for Production

npm run build
npm start

Running Tests

npm test

Usage

Calculating Option Price

1. Select "Calculate Option Price" mode
2. Choose option type (Call or Put)
3. Enter the following parameters:
   • Strike Price: The strike/exercise price of the option
   • Underlying Price: Current price of the underlying asset
   • Time to Expiration: Time until expiration in years
   • Risk-Free Rate: Risk-free interest rate (as percentage)
   • Volatility: Historical or implied volatility (as percentage)
4. Click "Calculate Option Price"

Calculating Implied Volatility

1. Select "Calculate Implied Volatility" mode
2. Choose option type (Call or Put)
3. Enter the following parameters:
   • Strike Price
   • Underlying Price
   • Time to Expiration
   • Risk-Free Rate
   • Market Option Price: The observed market price of the option
4. Click "Calculate Implied Volatility"

The calculator will use the Newton-Raphson method to find the volatility that produces the given market price.

Viewing History

• Recent calculations automatically appear below the main calculator
• Click any historical calculation to reload it into the results display
• History is limited to the 10 most recent calculations
• History is stored in browser localStorage and persists across sessions

Project Structure

frontend/
├── src/
│   ├── app/                    # Next.js app directory
│   │   ├── page.tsx           # Main calculator page
│   │   ├── layout.tsx         # Root layout
│   │   └── globals.css        # Global styles
│   ├── components/
│   │   ├── calculator/        # Calculator components
│   │   │   ├── CalculatorForm.tsx
│   │   │   └── ResultsDisplay.tsx
│   │   ├── history/           # History components
│   │   │   └── HistoryDisplay.tsx
│   │   └── ui/                # Shadcn UI components
│   ├── lib/
│   │   ├── black-scholes.ts   # Core BS calculation logic
│   │   └── utils.ts           # Utility functions
│   ├── services/
│   │   └── storage.ts         # LocalStorage service
│   └── types/
│       └── options.ts         # TypeScript type definitions
└── tests/
    ├── unit/                   # Unit tests
    │   └── black-scholes.test.ts
    └── integration/            # Integration tests
        ├── calculator.test.tsx
        └── history.test.tsx

Black-Scholes Model

The Black-Scholes model is used to calculate the theoretical price of European-style options. The model makes several assumptions:

• The underlying asset follows a geometric Brownian motion
• No dividends are paid during the option's life
• Markets are efficient (no arbitrage opportunities)
• Risk-free rate and volatility are constant
• European-style options (can only be exercised at expiration)

Formula

For a call option:

C = S₀N(d₁) - Ke^(-rT)N(d₂)

For a put option:

P = Ke^(-rT)N(-d₂) - S₀N(-d₁)

Where:

• C/P = Call/Put option price
• S₀ = Current stock price
• K = Strike price
• r = Risk-free rate
• T = Time to expiration
• σ = Volatility
• N(x) = Cumulative standard normal distribution

Testing

The project includes comprehensive test coverage:

• Unit Tests: Test core Black-Scholes calculations
• Integration Tests: Test UI components and user interactions
• Type Safety: Full TypeScript coverage ensures type safety

Run tests with:

npm test

Contributing

Contributions are welcome! Please ensure:

• All tests pass
• Code follows TypeScript best practices
• UI components maintain responsive design
• New features include appropriate tests

License

MIT

Acknowledgments

• Black-Scholes-Merton model by Fischer Black, Myron Scholes, and Robert Merton
• UI components from Shadcn UI
• Built with Next.js