Using the Monte Carlo (MC) simulation, evaluate at-the-money (i.e., the strike price is equal to the current stock price) European call and put options on an underlying stock with 2000, 4000, 6000, 8000, 10000, and 12,000 sample paths. Plot the call and put options prices against the number of sample paths. Now, determine the values of the call and put options applying the Black-Scholes (BS) option pricing model. Compare and explain the results obtained from the MC simulation and the BS model.