Monte Carlo Methods and Sümer?s New Jump Diffusion Processes and their Application in Gold Price

Abstract

This study aimed to execute Monte Carlo simulation method with Wiener Process, Generalized Wiener Process, Mean Reversion Process and Mean Reversion Jump Diffusion Process and to compare them and then expended with the idea of how to include negative and positive news shocks in the gold market to the Monte Carlo simulation. By enhancing the determination of the 3 standard deviation shocks within the process of Classic Mean Jump Diffusion Process, an enchanted model for the 1,96 and 3 standard deviation shocks were being used and additionally positive and negative shocks were added to the system in a different way. This new Mean Reversion Jump Diffusion Process that have been developed by Sümer, executes Monte Carlo simulation regarding the gold market return with five random variables that are chosen from Poisson distribution and one random variable chosen from the normal distribution. Additionally, by accepting volatilities as outlies over the 1,96 and 3 standard deviations with the effect of the new and good news and the standard deviations on the traditional approximate return and the standard deviations (volatility) and the obtained new approximate return and the new standard deviation (volatility) and compares them with the Monte Carlo simulations