Monte Carlo Simulation

You can choose to invest your money in one particular stock or put it in a savings account. Your initial capital is 1000 $. The initial stock price is 100 $. The interest rate r is 0.5% per month and does not change.

Your stochastic model for the stock price is as follows:

-next month the price is the same as this month with probability 1/2,

-with probability 1/4 it is 5% lower,

-and with probability 1/4 it is 5% higher.

This principle applies for every new month. There are no transaction costs when you buy or sell stock.

Your investment strategy for the next 5 years is:

-convert all your money to stock when the price drops below 95 $,

-and sell all stock and put the money in the bank when the stock price exceeds 110 $.

Describe how to simulate the results of this strategy for the model given.