Monte Carlo simulations are a set of algorithms which use a large number of calculations and repetitions to predict the behavior of complex random systems. We use them to estimate the values of an unknown variable using the principles of statistical inference. Monte Carlo methods are most commonly used to solve three classes of problems: integration, optimization and generation of random samples from a probability distribution. The problem we address in this thesis is the pricing of the derivatives using Monte Carlo simulations. As the prices of derivatives under certain assumptions can be calculated as an expectation, we estimate them by Monte Carlo integration. We use the Black-Scholes- Merton financial market model in which we model stock prices by geometric Brownian motion. We define the European call option, the Asian option and the Chooser option, and using Monte Carlo simulations we calculate the prices of these derivatives. To analyze the risks in the financial markets, we define the Greeks. Special methods are used to calculate the Greeks using Monte Carlo simulations. We briefly explain the pathwise method and use it to simulate the calculation of delta hedging for a portfolio consisting of European call options.