option pricing

Stock prices are modeled as geometric Brownian motion: dS = μS dt + σS dW. For a European call option, the payoff at expiry is max(S_T − K, 0).

MC price = e^(−rT) × average of simulated payoffs

Black-Scholes gives the exact closed-form price for European options. Monte Carlo converges to it, but MC generalizes to exotic options where no closed form exists.

references

Glasserman. "Monte Carlo Methods in Financial Engineering." Springer, 2003.

Longstaff & Schwartz. "Valuing American options by simulation." Review of Financial Studies, 2001.