Black-Scholes & Stochastic Calculus

Analytical valuation of European options and exact computation of sensitivity Greeks ($\Delta, \Gamma, \Theta, \nu, \rho$) with MLX accelerated Monte Carlo GBM path simulation.

OPTION PARAMETERS

SPOT PRICE (S):

STRIKE PRICE (K):

TIME TO EXPIRY T (YEARS):

VOLATILITY σ (%):

RISK-FREE RATE r (%):

CALL PRICE

$4.58

DELTA (Δ)

0.461

GAMMA (Γ)

0.028

VEGA (ν)

0.281

THETA (Θ)

-0.021

RHO (ρ)

0.198

GBM MONTE CARLO PRICE PATHS (S0 = 100)