Quant · Jan 2026
Options Pricing Engine and Greeks Computation
Black-Scholes closed-form and Monte Carlo pricers with 100K antithetic paths for European equity options. Delta, Gamma, and Vega are computed both analytically and via finite differences across strike and maturity grids.
100K antithetic
MC paths
Δ, Γ, Vega
Greeks
BS, MC
Pricers
Problem
I sought to develop a transparent and validated pricing stack in which every assumption (volatility, rate, maturity, path count) is explicit and in which sensitivities can be cross-verified through two independent methods.
Approach
I implemented a Black-Scholes closed-form pricer alongside a Monte Carlo pricer using 100K antithetic paths. I computed Delta, Gamma, and Vega both analytically and via finite differences across strike and maturity grids, and quantified Monte Carlo noise by moneyness and maturity.
Results
The result is a reusable pricer accompanied by sensitivity diagnostics. The analysis identifies regimes in which Monte Carlo estimates become unstable and regions where finite differences diverge from analytical Greeks, providing useful insight for model validation work.
Stack