Application of Monte Carlo simulation method to stochastic finance arguments: Option pricing

The majority of mathematical models used in natural sciences and economics are formed by differential equations. However, the assumptions are mostly based on the assumption that the inputs of the system are fully known and that the measurements are made precisely. Such models are called deterministic models and can only make a limited description of the system. By using probability theory, uncertainties arising from measurements and initial conditions are expressed in terms of noise in differential equations. Such equations are called stochastic differential equations. In financial markets, investors avoid risk. Financial products in the Derivative Markets were produced for this purpose. Pricing of these products is an important problem to protect the rights of both parties. Therefore, simulation of models with Geometric Brown process, where uncertainties are involved in pricing, is an important step to solve the problem. The main purpose of this study is to reveal the differences between the option premiums used in the pricing of options, which is one of the financial derivatives, by using Black-Scholes method and Monte Carlo method. The calculations made in this study showed that there is no significant difference between Monte Carlo and Black-Scholes models in terms of option premiums.