multi-method-bs-pricing

A Python package for pricing European and American options via the Black-Scholes equations using five independent methods: analytic (Black-Scholes formulas), binomial tree, Monte Carlo, finite differences, and a physics-informed neural network. Each method supports continuous dividend yield and computation of the Greeks.

Installation

pip install multi-method-bs-pricing

The PINN pricer requires TensorFlow, which is an optional extra:

pip install "multi-method-bs-pricing[pinn]"

Example

from bspricepal import Option, analytic_bs_pricer, binomial_pricer, mc_pricer, fd_pricer

option = Option(
    S0=100.0,      # spot
    K=105.0,       # strike
    T=1.0,         # years to expiry
    r=0.05,        # risk-free rate
    sigma=0.2,     # volatility
    div_yield=0.0,
    option_type="call",     # "call" | "put"
    exercise="european",    # "european" | "american"
)

print(analytic_bs_pricer(option))
print(binomial_pricer(option, n_steps=500))
print(mc_pricer(option, n_paths=100000, n_steps=100))
print(fd_pricer(option, n_space=400, n_steps=400))

Greeks

Exact solution for European options:

from bspricepal import analytic_bs_greeks

print(analytic_bs_greeks(option))

Finite difference approximation for any pricer, particularly for American options:

from bspricepal import all_greeks, delta, binomial_pricer

print(all_greeks(binomial_pricer, option, n_steps=500))
print(delta(binomial_pricer, option, h=1e-2, n_steps=500))

Individual Greeks available: delta, gamma, vega, rho, theta.

API