Numerical Methods
Derivatives Pricing Engine
An object-oriented engine of sixteen pricers for vanilla and exotic options across six stochastic processes, spanning analytic, lattice, finite-difference, COS Fourier, and Monte Carlo methods behind a self-registering registry and a Streamlit dashboard.
Prices vanilla, American, Asian, barrier, and basket options over GBM, Heston, Bates, SABR, Dupire local-volatility, and rough-Bergomi processes, the last through an O(N log N) hybrid FFT scheme, each self-registering through a pricer and process registry.
Combines Black-Scholes and Merton analytics, COS Fourier pricing, batched CRR trees, explicit, implicit, and Crank-Nicolson finite differences with projected SOR, and Monte Carlo with Longstaff-Schwartz exercise and an adaptive multilevel variant.
Cuts Monte Carlo variance with antithetic variates, Brownian-bridge-ordered Sobol QMC, control variates, and common random numbers, computes Greeks by analytic, pathwise, likelihood-ratio, lattice, and bump methods, calibrates Heston, SABR, and SVI surfaces, and warms 49 Numba JIT kernels at import.