Options Greeks & Delta-Hedging Simulator

This repository contains two self-contained Jupyter notebooks that illustrate key concepts in derivatives risk management using the Black–Scholes framework and Monte Carlo simulation.

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📘 Notebooks

1. greeks_visualization.ipynb

• Implements Black–Scholes pricing formulas for European calls and puts.
• Derives and visualizes the main option Greeks:
  • Delta (Δ), Gamma (Γ), Vega (ν), Theta (Θ), Rho (ρ).
• Produces 3D surfaces and 2D cross-sections showing how Greeks depend on:
  • Stock price relative to strike.
  • Time to maturity.
• Includes put–call parity checks and interpretations of Greek behavior (e.g. Gamma peaks near ATM, Vega grows with √T).

2. delta_hedging.ipynb

• Simulates stock price paths under Geometric Brownian Motion (GBM).
• Implements a discrete delta-hedging strategy:
  • Start long 1 option, short Δ shares.
  • Rebalance stock position each step as Δ changes.
  • Track a self-financing cash account.
• At maturity:
  • Close the hedge.
  • Compare hedge performance vs option payoff.