Monte Carlo studies of American type call options with discrete time (Q2740073)

The author deals with the structure of the stopping domain for different types of payoff functions, in particular, standard linear, piecewise linear, quadratic, stepwise and logarithmic for American type options in discrete time. The studies are based on the Monte Carlo method and the underlying stock is modelled by the geometrical random walk with multiplicative increments with log-normal distribution. To study the stopping domain the upper and the lower threshold values of the initial stock price are set. By simulating a large number of trajectories for each stock price on the grid the expected profit of the option is evaluated. If the expected profit is less than the profit for the given stock price at the given moment, then the stock price is in the stopping domain. The author analyzes the results of the algorithm by investigating the probability of classification errors. The results of experiments are presented.