option-pricer

Black-Scholes-Merton option pricer with Greeks and Monte Carlo simulation, served via a Streamlit interface.

Features

• Analytical BSM pricing — closed-form solution for European calls and puts
• Full Greeks — Δ Delta, Γ Gamma, Θ Theta, ν Vega, ρ Rho
• Monte Carlo — GBM simulation with antithetic variates variance reduction, 95% confidence intervals
• Convergence analysis — log-scale plot showing MC estimate converging to analytical price
• Greeks vs Spot — visualise Delta, Gamma, Theta as spot price varies
• Vol surface — 3D BSM price surface over strike × tenor

Usage

pip install -r requirements.txt
streamlit run app.py

Structure

option-pricer/
├── pricer.py        # Core BSM and Monte Carlo logic (no UI dependency)
├── app.py           # Streamlit frontend
└── requirements.txt

Model notes

The Black-Scholes-Merton model assumes:

• Constant volatility (no smile/skew)
• Log-normal distribution of returns
• Continuous risk-free rate, no dividends
• European-style exercise

Monte Carlo uses antithetic variates to reduce variance by ~30–50% vs naive sampling.

Greeks interpretation

Greek	Meaning
Δ Delta	Price sensitivity to ±1 unit move in spot
Γ Gamma	Delta sensitivity to ±1 unit move in spot
Θ Theta	Price decay per calendar day
ν Vega	Price sensitivity to ±1% move in implied vol
ρ Rho	Price sensitivity to ±1% move in risk-free rate