Monte Carlo Simulation

In: Business and Management

Submitted By ajjuiitm
Words 3279
Pages 14
Monte Carlo simulations and option pricing by Bingqian Lu Undergraduate Mathematics Department Pennsylvania State University University Park, PA 16802 Project Supervisor: Professor Anna Mazzucato July, 2011

Abstract Monte Carlo simulation is a legitimate and widely used technique for dealing with uncertainty in many aspects of business operations. The purpose of this report is to explore the application of this technique to the stock volality and to test its accuracy by comparing the result computed by Monte Carlo Estimate with the result of Black-Schole model and the Variance Reduction by Antitheric Variattes. The mathematical computer softwear application that we use to compute and test the relationship between the sample size and the accuracy of Monte Carlo Simulation is itshapeMathematica. It also provides numerical and geometrical evidence for our conclusion.

0.1

Introduction to Monte Carlo Simulaion

Monte Carlo Option Price is a method often used in Mathematical finance to calculate the value of an option with multiple sources of uncertainties and random features, such as changing interest rates, stock prices or exchange rates, etc.. This method is called Monte Carlo simulation, naming after the city of Monte Carlo, which is noted for its casinos. In my project, I use Mathematica, a mathematics computer software, we can easily create a sequence of random number indicating the uncertainties that we might have for the stock prices for example.

0.2

Pricing Financial Options by Flipping a Coin

A distcrete model for change in price of a stock over a time interval [0,T] is √ Sn+1 = Sn + µSn ∆t + σSn εn+1 ∆t, S0 = s (1) where Sn = Stn is the stock price at time tn = n∆t, n = 0, 1, ..., N − 1, ∆t = T /N , µ is the annual growth rate of the stock, and σ is a measure of the stocks annual price volatility or tendency to fluctuate. Highly volatile…...

Similar Documents

Interpretation of Modeling and Simulation

...Interpretation of Modeling and Simulation Can there be a better fit for a company out there that uses Microsoft Excel to conduct modeling to simulate their business growth other than Microsoft itself? Microsoft has made billions of dollars selling their Microsoft Office Suites and their home computer operating systems around the world. They have become one of the largest and well known companies in the world. The way that I see it, is that Microsoft’s business model, in a nutshell, is to provide goods and services in the form of software and support to paying customers. One question that may be asked in this day an age is with the advances in cloud computing and Google’s “free” gadgets, will the traditional Microsoft’s business model come to an end? What will Microsoft’s business analysts do in order to change their business model? One can only imagine that it will need to be modeled and simulated first to avoid potentially expensive mistakes. I must start off by saying that before I started my Systems Modeling Theory online class through Strayer, I thought that it may just be one of the hardest classes to understand that I’ve ever taken throughout the course of my college career. I can say now after having completed the last nine weeks of class that I was correct. What’s hard, is not understanding the concepts of why businesses would use Excel models for their business growth but rather the actual use of Excel itself. With all of the bells and......

Words: 1781 - Pages: 8

Monte Carlo

...Monte Carlo Simulation Tutorial This tutorial shows how to use Microsoft Excel to develop Monte Carlo simulations without the use of add-ins or special software (such as @RISK or Crystal Ball). (Note, however, that there are some important advantages of using these dedicated software packages.) After completing the tutorial you should have a sufficient understanding of Monte Carlo concepts and Excel capabilities to begin building your own Monte Carlo simulations applied to a wide range of business problems, including the construction of short-term profit plans (otherwise referred to as “Cost-Volume-Profit” models, covered in Chapter 9 of the text). Monte Carlo refers to a widely used approach for solving complex problems using computer algorithms to simulate the variables in the model (e.g., a CVP model). Typically, an algorithm is developed to "model" the problem, and then the algorithm is run many times (from a few hundred up to millions) in order to develop a statistical data set for how the model behaves. Simple Example: Tossing a “Fair” Coin—Heads vs. Tails? For the simplest example, consider the basic coin toss. This is a process which has two possible outcomes (heads or tails), each with a 50% probability. In a million coin tosses, roughly half will be “heads” and half will be “tails.” A simple Monte Carlo simulation would support this conclusion. If you were to develop a spreadsheet with a random number generator resulting in 0 for “heads” and 1 for “tails,”......

Words: 2387 - Pages: 10

Value at Risk & Historical Simulation

...past data over a specific period of time and checking the frequency of losses exceeding the VAR amount. It can be computed using the following formula. Stress testing should always complement VAR. Historical Simulation This method employs historical returns data to assemble the cumulative distribution function, and does not place any assumptions on the shape of the distribution. A historical simulation simply sorts the returns by size. If the sample include 100 returns, the value at risk at a confidence of 95% is the fifth largest loss. Several criticisms are often made of this approach. Two portfolios with same VAR may have very different expected shortfall. ■Historical simulation assumes that returns are independent and identically distributed. This not necessarily the case; real-world data often displays volatility clustering. ■Returns in the recent-past and far-past are given equal weighting. However, recent returns have greater bearing on future behavior than older returns. ■This method requires a large set of historical data for accuracy; this, however, is not always available. ■Because the method is entirely reliant on historical data, the result cannot be influenced by subjective information (as with Monte-Carlo simulation). This may be significant if a fund manager predicts large changes in the business environment....

Words: 636 - Pages: 3

Simulation

...INTRODUCTION: The purpose of this paper is to bring out the use of Simulation by Managers of various organizations. Under discussion will be:  Definition of simulation.  Model construction.  When and why it becomes handy to use simulation.  Steps used in simulation technique.  Random selection in simulation.  Advantages / benefits derived from use of simulation technique.  Disadvantages /Challenges associated with simulation technique.  Role of computer in simulation.  Conclusion / comments. Definition of simulation: Simulation can be defined as a quantitative technique which describes a process by developing a model of that process and then conduct a series of organized trial and error experiments to predict the behavior of the process through time often with the aid of a computer. It is a method that is used to solve a problem in many areas of management, for example inventory management, queuing problems, profit analysis and project management among others. Model construction: A successful simulation model has to be carefully designed in order to achieve the intended predictive purpose. Therefore important factors have to be considered such as; i. It must be objective oriented. It must be constructed for a purpose and be able to achieve that purpose. ii. Critical variables and relationships. These must be identified and incorporated in model. However it is not essential or indeed desirable to include all variables in the model. iii. Simplicity...

Words: 1498 - Pages: 6

Using a Combined Method of Hierarchical Analysis and Monte Carlo Simulation in Order to Identify and Prioritize the Target Market Selection Criteria

...Applied mathematics in Engineering, Management and Technology 2 (2) 2014:466-475 www.amiemt-journal.com Using a combined method of hierarchical analysis and Monte Carlo simulation in order to identify and prioritize the target market selection criteria (Case study: Food distribution companies of Mashhad-Iran) Amir kariznoee Ph.D. student of Industrial Management,University of Mazandaran ,Iran (Corresponding Author's E-mail: Amir.kariznoee@yahoo.com) Monireh Bijandi Graduate of Accounting in Ferdowsi University of Mashhad,Iran Mahdi Ghayur Maddah Student of Public Management in Ferdowsi University of Mashhad,Iran Vajihe Mogharabi M.A. Student of Information Technology Management, Shahid beheshti University,Tehran,Iran Abstract The aim of this study is to identify and prioritize the key factors in selecting a target market in the food industry. In order to determine the components and subcomponents of this study, we have used previous researches in this area. In order to match these factors with the food industry situation and create a hierarchical structure, we have obtained the opinions of 323 experts about affecting factors on choosing a market in this industry with the use of questionnaire. Then, using a combination of hierarchal analysis process and Monte Carlo simulation and cooperation with 10 senior executives of distribution companies, the weight of each component and sub-component was determined. In general, four components and ten sub-components......

Words: 3589 - Pages: 15

Monte Everest

...estrategia, cambiar el objetivo de llegar a la cima por el objetivo de garantizar la supervivencia del grupo y retomar la “expedicion” al siguiente dia o cuando mejore el clima. | Elegir acciones para acabar con la crisis | 1.- Centrar la atención en resolver rápidamente la crisis | Ambos equipos, al ver que se avecinaba una tormeta y que el clima empeoraba debieron optar por descender la montaña lo mas rapido posible. | 2.- Disciplina en las decisiones del equipo con el fin resolver la crisis | La disciplina en este punto vino por la parte de los lideres ya que fueron ellos quienes faltaron a ella. Ambos lideres debieron entregar la responsabilidad a quien estaba en mejores condiciones de decidir una nueva estrategia. | GRAFICA DEL MONTE EVEREST Y SU PROCESO DE ESCALAMIENTO A TRAVES DE LOS 5 CAMPAMENTOS QUE LA COMPONEN...

Words: 786 - Pages: 4

Simulation Modeling

...Brooklyn Warren Chapter 10 Simulation Modeling What is Simulation? * To try to duplicate the features, appearance, and characteristics of a real system. * Imitate a real-world situation mathematically. * Study its properties and operating characteristics. * Draw conclusions and make action decisions based on the results. Processes of Simulation: 1. Define Problem 2. Introduce Important Variables 3. Construct Simulation Model 4. Specify Values of Variables to Be Tested 5. Conduct the Simulation 6. Examine the Results 7. Select Best Course of Action Advantages of Simulation: * Straightforward and flexible. * Can handle large and complex systems. * Allows "what-if" questions. * Does not interfere with real-world systems. * Study interactions among variable. * "Time comparison" is possible. * Handles complications that other methods can't. Disadvantages of Simulation: * Can be expensive and time consuming. * Does not generate optimal solutions. * Managers must generate all conditions and constraints. * Each model is unique. Monte Carlo Simulation: Can be used with variables that are probabilistic. Steps: * Establish the probability distribution for each random variable. * Use random numbers to generate random values. * Repeat for some number of replications. Probability Distributions: Historical data Goodness-of-fit tests for common......

Words: 259 - Pages: 2

Monte Carlo Analysis

...Monte Carlo Statistical Analysis Name Course Instructor Date The Monte Carlo method is a mathematical method used for problem solving through the generation of random numbers and then observing a fraction of these numbers and the properties they obey. It is useful in obtaining numerical solutions to problems that are too complicated for analytical solutions. It is a form of probability used to understand the impact of risk and uncertainty in various areas such as financial and cost forecasting. It involves computation of the likelihood of given events occurring or not occurring, without taking into account the interaction of the elements involved in influencing the occurrence. The mathematical method was invented by Stanislaw Ulam in 1946 and named by Nicholas Metropolis after a classy gambling resort in Monaco, where a relative of Ulam frequently gambled [ (Fishman, 1996) ]. Concepts of the Monte Carlo method Uncertainty Being a forecasting model, there are assumptions that need to be made due to the uncertainty of various factors. One therefore needs to be able to make estimations of the expected results as they cannot predict with certainty what the end value will be. Important factors such as historical data and past experiences in the field can be helpful in making an accurate estimate. Estimation In some cases, estimation may be possible but in others it is not. In situations where estimation is possible, it is wise to use a wide range of possible values......

Words: 2486 - Pages: 10

Abc Monte Carlo

...Company Analysis: Monte Carlo Overview of Indian Economy According to National Council of Applied Economic Research (NCAER) the fourth largest economy of the world, i.e. India is expected a growth rate of 5.1% to 5.5% in real GDP in 2015. Moreover Technopak Report 2014 says, textile and apparel industry has been a major contributor to India’s GDP from last two decades, providing employment to more than 45M people. This sector has also contributed towards the growth of industrial production and foreign exchange through exports. Textile and Apparel Industry In developing countries like India, higher annual GDP growth corresponds to increase in purchasing power of the consumers, favouring the growth in textile and apparel industry. But in developed countries USA, Japan and countries of European Union slower annual GDP growth corresponds to reducing the demand for textile and apparel. Cheap labour in developing countries accounts well for their production advantage. The size if Indian textile and apparel industry has increased substantially from US $70 billion in 2006 to US $90 billion in 2013. (Source: Technopak Report 2014) Overview Monte Carlo was launched in 1984 as an exclusive woollen brand, since then it has been a leading apparel brand in India in terms of revenue. Monte Carlo has successfully established as a Superbrand in each section consumers, viz. Men, Women and Kids. It primarily caters to premium and mid-premium segments among the above 3 consumer......

Words: 373 - Pages: 2

Cmgt442 Week 4 Individual Assignment Monte Carlo Method Cmgt 442 Week 4 Individual Assignment Monte Carlo Method

...are the major issues to consider?     CMGT 442 Week 3 Supporting Activity Security Risks   Discuss the considerations necessary to address the possible security requirements and the possible risks associated with the Benefits Elections Systems being requested by the Service Request.     CMGT 442 Week 3 Learning Team Assignment Risk Assessment Week 3 Project Report   Submit the following items to your facilitator:   A team progress report to your instructor explaining what your team accomplished during the week, challenges your team faced, and potential approaches to the Final Learning Team Project     CMGT 442 Week 4 Individual Assignment Monte Carlo Method   Recreate the simulation presented in the "Performing Monte Carlo Simulation" video.   Submit the Microsoft® Excel® spreadsheet along with a 1- to 2-page explanation on how the Monte Carlo tool can be used in risk assessment.     CMGT 442 Week 4 Supporting Activites   CMGT 442 Week 4 Supporting Activity Decision Tree   Use Microsoft® Visio®, PowerPoint®, or Word to create a decision tree diagram for the selection of a cell phone. Address risk in your decision tree.   CMGT 442 Week 4 Supporting Activity Risk Breakdown Structure   Develop a list of risk breakdown structure (RBS) categories for this purpose. Justify each category within your RBS.   CMGT 442 Week 4  Learning Team Assignment Risk Assessment Week 4 Project Report   Submit the following items to your facilitator:   A team progress report to your instructor......

Words: 957 - Pages: 4

Monte Carlo Simulation

...Monte Carlo Simulation The Monte Carlo Simulation encompasses “any technique of statistical sampling employed to approximate solutions to quantitative problems” (Monte Carlo Method, 2005). The Monte Carlo method simulates the full system many times, each randomly choosing a value for each variable from its probability distribution. The outcome is a probability distribution of the overall value of the system calculated through the iterations of the model. A standard approach to risk management of projects is outline by Project Management Institute (2004) that includes six processes: Risk Management Planning, Risk Identification, Risk Qualification, Risk Quantification, Risk Response Planning, and Risk Monitoring and Control. Monte Carlo is usually listed as a method to use during the Risk Quantification process to better quantify the risks to the project manager is able to justify a schedule reserve, budget reserve, or both to deal with issues that could adversely affect the project. Monte Carlo simulation, while not widely used in project management, does get some exposure through certain project management practices. This is primarily in the areas of cost and time management to quantify the risk level of a projects budget or planned completion date. In time management, Monte Carlo simulation may be applied to project schedules to quantify the confidence the project manager should have in the target competition date or total project duration. In cost management, the......

Words: 976 - Pages: 4

Carlos Slim

...Carlos Slim Helu In 1902, Julián Slim Haddad, father of Carlos Slim Helú, arrived to Mexico from Lebanon. He was escaping from the Ottoman Empire, which at the time conscripted young men into its army. One of the markers of Carlos Slim Helu’s success has been his ability to buy and sell at the correct times. His investments in the downturn of the 1980s were the foundation of his wealth, and throughout the 1990s he continued to sell businesses which were successful then use the return to invest in others which were up and coming. Carlos Slim was born on january 28, 1940. He completes his professional studies in civil engineering at the UNAM. By 1965 Carlos Slim aquired companies like inmobiliaria Carso, casa de bolsa inversora Bursátil, embotelladora Jarritos del sur, and some others. Carso was incorporated in January 1966. Carso comes from the first syllable of the names Carlos and Soumaya, Mr. Slim's wife. The Mexican economic crash of 1982 was what delivered the opportunity to consolidate his wealth. In 1990, Grupo Carso and other Mexican investors acquired 10.4% of the companys stock, in partnership with SBC - 5% with an option for an additional 5% - and France Telecom 5%. Since 1990, Telmex has embraced a work culture where training, modernization, quality and customer service is a priority. Ten principles of grupo Carso. 1. Have always simple organizational structures, minimal hierarchical levels; provide human and in-house development of the executives;......

Words: 465 - Pages: 2

Using Monte Carlo Tool for Risk Assessment

...Using Monte Carlo Tool for Risk Assessment CMGT/442 March 21, 2016 Craig McCormick Using Monte Carlo Tool for Risk Assessment A project can have many variables that can prevent it from completion. No one variable can effect a project more than a project’s risks. The key to having a successful completion of a project is through a risk assessment. It is the project manager’s job to identify potential risks within a project. Identifying these uncertainties will help to minimize the risks and their impact on the project. The Monte Carlo tool can be an asset for a project manager and risk assessment process. What is Monte Carlo? Monte Carlo is a simulation of mathematical technique that analyzes risk for decision making. The simulation uses different choices of action and gives a variety of probabilities and possible outcomes based on those actions. These possible outcomes are given in the most extreme situations, as well as with minor decisions. Additionally, the Monte Carlo simulation provides possible consequences of conservative decisions. Overall, “Monte Carlo analysis involves determining the impact of the identified risks by running simulations to identify the range of possible outcomes for a number of scenarios.” (Marom, 2010) How Monte Carlo Works Project risks are one of the big unknowns when it comes to risk assessment. Monte Carlo attempts to change these unknowns by using probability distributions. Probability distributions show that each risk variable...

Words: 444 - Pages: 2

Order Book Simulations Using Monte Carlo Methods

...Modeling Order Book Fluctuation by Monte Carlo Technique CONTENTS Page no. 1) Certificate 2 2) Acknowledgement 3 3) Abstract 5 4) Introduction 6 5) Simulation code 8 ➢ Order Book 8 ➢ Diffusion 9 ➢ Price and Annihilation 11 ➢ One Trade return 14 ➢ Waiting time between consecutive trades 16 ➢ Conditional return 19 ➢ Hurst curve 20 6) Results and Discussion 22 7) Summary 28 8) Future Prospects 29 9) References ...

Words: 1053 - Pages: 5

Methos of Carlo

...provide well - behaved experimental systems are increasingly providing a bridge between theory and experiment, for instance; the Monte Carlo method (MC) and the molecular-dynamics method (MD). In Monte Carlo method the exact dynamical behavior of a system is replaced by a stochastic process, whereas the MD methods are based on a simpler principle and consists of solving a system of Newton's equations for an N-body system. Stochastic simulation is some times called MC simulation (simulation is a numerical technique for conducting experiment on a digital computer, which involves certain types of mathematical and logical models that describe the behavior of the system over extended period of real time). The generally accepted birth date of the MC method is 1949, when an article entitled "The Monte Carlo Method" appeared, the American mathematicians J.Neyman and S.Ulam are considered to be its originator. The first successful application of this method to a problem of statistical thermodynamics dates back only to 1953, when Metropolis and co-workers studied "fluid" consisting of hard disks. In the nineteenth and early twentieth centuries, statistical problems were sometimes solved with the help of random selections, that is, in fact, by the MC method. Prior to the appearance of electronic computers, this method was not widely applicable since the simulation of random quantities by hand is a very laborious process. Thus, the beginning of the MC method as a highly universal......

Words: 372 - Pages: 2