options-pricing

To compute Black-Scholes option prices and Greeks, supply underlying price, strike, maturity, risk-free rate, and volatility. The Skill calculates European call/put prices alongside analytical Delta, Gamma, Vega, Theta, and Rho using the Black-Scholes-Merton formulation.

Pricing American options with early exercise is best handled using the Cox-Ross-Rubinstein binomial tree. This Skill models early exercise features through backward induction on the tree to accurately value American contracts.

To extract implied volatility from observed market option prices, this Skill applies Brent's method root-finding. It recovers implied volatility and validates the results against arbitrage bounds to ensure pricing accuracy.

Yes, you can use Monte Carlo simulation for options pricing with variance reduction. This Skill estimates prices via Geometric Brownian Motion simulation using antithetic variates and control variates, providing standard errors and confidence intervals.

To generate and visualize an implied volatility surface, this Skill constructs a heatmap and smiles across strikes and maturities. It uses matplotlib to plot the extracted implied volatility data for market analysis.

Yes, this options pricing tool requires numpy and scipy to run its numerical methods. These dependencies support the underlying mathematical computations for Monte Carlo estimation, root-finding, and analytical Greek calculations.