Add Black-Scholes Option Pricing Algorithm in R

[iampratik13]

This PR introduces an educational and well-documented implementation of the Black-Scholes-Merton model for European option pricing in R.

Overview
The implementation provides a comprehensive R6-based BlackScholesCalculator class that supports:

• Call and Put option price calculations
• Computation of Greeks (Delta, Gamma, Theta, Vega, Rho)
• Implied volatility estimation via the Newton-Raphson method

Key Features

• Modular and extensible R6 OOP design
• Input validation for robustness
• Clear financial and mathematical documentation
• Example demonstration for reproducibility

Usage
Run demonstrate_black_scholes() to view the pricing results and Greeks for sample parameters.

Complexity

• Time Complexity: O(1) for pricing and Greeks computation
• Space Complexity: O(1)

This implementation enhances the repository’s finance module with a fundamental model widely used in quantitative finance and derivatives analysis.

[Copilot]

Pull Request Overview

This PR introduces a comprehensive implementation of the Black-Scholes-Merton model for European option pricing in R. The implementation provides a modular R6-based calculator class that supports option pricing, Greeks computation, and implied volatility estimation.

Key changes:

• Adds a complete BlackScholesCalculator R6 class with call/put pricing methods
• Implements Greeks calculation (Delta, Gamma, Theta, Vega, Rho) for both call and put options
• Includes implied volatility estimation using Newton-Raphson method with robust convergence handling