This project calculates the Black-Scholes option pricing formula, derives the Greeks, and visualizes the implied volatility surface for a given stock ticker.
Options traders often use implied volatility to understand market expectations of future price movement. This tool automates the process of:
- Pulling real market data for a given ticker (limited to AAPL without an API key)
- Pricing European-style call options using the Black-Scholes formula
- Deriving key Greeks: Delta, Gamma, Vega, Theta, and Rho
- Computing implied volatility using the Newton-Raphson method
- Plotting a 3D implied volatility surface over time to expiry and moneyness
- ✅ Analytical Black-Scholes pricing
- ✅ Calculation of all major option Greeks
- ✅ Implied volatility solver using numerical methods
- ✅ 3D volatility surface visualization
- ✅ Built-in support for dividend yield and interest rates
- ✅ Modular code structure for easy extension
numpypandasmatplotlibplotly(optional for interactive 3D graphs)jax(for automatic differentiation and gradient computation)- Market data access library (custom or from
MarketData.com)
-
Fetch Option Chain
Pulls live market data fromMarketData.com. Without an API key, only Apple (AAPL) is supported. -
Compute Black-Scholes Price & Greeks
Uses closed-form solutions to compute option price and sensitivities. -
Estimate Implied Volatility
Solves for the implied volatility that matches the market price using Newton-Raphson iterations: $$ \sigma_{n+1} = \sigma_n - \frac{f(\sigma_n)}{f'(\sigma_n)} $$ -
Plot the Volatility Surface
Displays a 3D surface of implied volatilities as a function of moneyness and time to expiry.
- Option Chain with calculated IV
- 3D Volatility Surface:
- X-axis: Moneyness ( \frac{S}{K} )
- Y-axis: Time to Expiry (Years)
- Z-axis: Implied Volatility
This repo is designed for educational purposes, helping users learn about:
- Derivatives pricing models
- Sensitivity analysis in options
- Numerical root-finding methods
- Data visualization in quantitative finance