Monte Carlo Simulation In Decision Making

MONTE CARLO SIMULATION IN DECISION MAKING ABSTRACT Monte Carlo simulation in simple terms is solving a problem or as an alternative solution using a probability or probability system or simply what we call opportunities. One of the applied fields that uses Monte Carlo simulation a lot is the financial sector because Monte Carlo simulation uses a number of experiments (taking data) from an existing range and distributes it and then sees how many opportunities will appear in that range. Keywords: monte carlo simulation, probability A. Introduction Simulation is a tool in statistics that is used to generate data with predetermined limits. This Monte Carlo simulation is a quantitative risk assessment technique, which means that in its implementation, this simulation uses many number systems and data probability ratios. One applied field that widely uses Monte Carlo simulation is the financial sector. Monte Carlo simulation is used to simulate no-arbitrage derivative pricing estimates when there is no closedform solution in more complex models such as volatility and GAR-CH models. Boyle (1977) first used Monte Carlo Simulation in this area. Many modifications to the Monte Carlo simulation have been made to increase the precision of this simulation. There are several modifications of Monte Carlo simulation, such as the Quasi Monte Carlo method, Control Variate, and Moment Matching. B. Definition of Monte Carlo Simulation The meaning of the term Monte Carlo is often considered the same as probabilistic simulation. Monte Carlo more strictly selects numbers randomly from a probability distribution to run the simulation. Monte Carlo simulation can also be defined as a method to assist decision making by analyzing and creating models in a system that contains risk and uncertainty. This simulation analyzes a system randomly for each variable from its probability distribution. It can also be understood that Monte Carlo simulation is a probabilistic simulation where a solution to a problem is given based on a randomization process. It is said that it is widely used in the world of finance because in the world of finance and banking, Monte Carlo simulation is certainly needed to calculate financial risk. For banks, one of whose main activities is providing credit to customers, of course Monte Carlo is needed to predict banking financial risks due to bad credit. In the world of investment, investors can use Monte Carlo simulations to determine the risk of default on an investment instrument. Basically, in the world of finance and banking, Monte Carlo simulation can help. C. Application of Monte Carlo Simulation in Case Examples Samsung company managers in Indonesia are deciding how many laptops to order each week from the parent company in Korea. One of the main considerations in this decision is the number of consumer requests each week. The laptop will be sold for Rp. 12,500,000.00. The number of laptop requests is a random variable (considered X) that ranges from ) to 4 per week. From available records, the manager has determined the frequency of laptop requests for the last 100 weeks and that data is as follows: • Step 1: establish a probability distribution Laptop demand per Frequency of Probability week demand distribution 0 20 20/100=0,20 1 40 40/100=0,40 2 20 20/100=0,20 3 10 10/100=0,10 4 10 10/100=0,10 amount 100 1,00 • Step 2: calculate the cumulative distribution • Step 3: assign an interval of random numbers for each variable Laptop demand Probability Cumulative per distribution of probability Interval of random numbers week demand, (px) 0 0,20 0,20 0-19 1 0,40 0,60 20-59 2 0,20 0,80 60-79 3 0,10 0,90 80-89 4 0,10 1,00 90-99 amount 1,00 • Step 4: form/select random numbers (generating random numbers) For random numbers we can use Microsoft Excel software by using the randbetween command. D. Monte Carlo Simulation Application in Excel • Step 4: form/select random numbers (generating random numbers) For random numbers, we can use Microsoft Excel software by using the randbetween command. For example, the number of frequencies is 100, then we write Randbetween (1;100) After getting a random number and determining the chosen random number, then choose a number that is in the same column. Laptop demand per Random week interval 0 0-19 number Random number (R) 1 20-59 2 60-79 3 80-89 4 90-99 R=39 amount • Step 5: the fifth step can be shown in the following table, for example the demand for 5 consecutive weeks is: Week to Random number Demand, X Revenue (RP) (R) 1 39 1 12.500.000,00 2 73 2 25.000.000,00 3 72 2 25.000.000,00 4 75 2 25.000.000,00 5 37 1 12.500.000,00 amount 8 100.000.000,00 The results of this simulation can be concluded: estimated average demand for laptops= 31/15=2.07 per week. Estimated average income of PT Samsung Indonesia= Rp. 100,000,000.00/5= Rp. 20,000,000.00 per week E. Conclusion The conclusion of this article is that Monte Carlo simulation is widely used in companies because the system is quite long and complicated. However, simply in organizations, this Monte Carlo simulation can be used in long-term decision making. By looking at the probability or possibility of how far the organization will develop, Monte Carlo simulation is the right one to use. To better understand how Monte Carlo simulations work, we can read similar journals or books that discuss decision making or can also visit the sites listed in the bibliography of this article.