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.