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Monte Carlo Simulation : A Computerized Mathematical Technique

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I. Introduction The Monte Carlo Simulation is a computerized mathematical technique that allows people to account for risk in quantitative analysis and decision. It furnishes the decision-maker with a range of possible outcomes and probabilities that they will occur for any chance of action. It shows the extreme possibilities of things as well. The system calculates results over and over, each time using a different set of random values from the probability functions. The simulation could involve tens and thousands of recalculations before its complete. There will be many different probability distributions. In this exploration I will find how to use the Monte Carlo Simulation in order to find future stock prices for the Gold Share Market (GLD). II. Exploration First, we need to go in depth and see what we need to find in order to start the simulation. Each day, the the price of an asset, such as a stock is: Today’s Stock Price= Yesterday’s Stock Price x er r=periodic daily return, the rate that the asset increased or decreased that day. Because the rate of return on an asset is a random number, to model the movement to determine possible future values, a formula is needed that model random movements. This was first done about 100 years ago by Louis Bachelier who first applied the Brownian Motion; a formula used to model random movements and physics to the movement of the price of an asset. His work expanded on the Black Scholes Finance formula, and some of

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