...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...
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...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 project...
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...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 ...
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...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 were...
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...can have some fun coming up with an educated guesstimate by going to the Paul Beeson Physician Faculty Scholars in Aging Research Program Here's how: type in Beeson-- beeson.org/livingto100 – if only we could --/quiz.htm. The life expectancy calculator asks 23 questions ranging from do you smoke to eating habits to a little family history. According to the calculator, I can expect to live a fraction more than the male average of 84 years. Obviously you really can't predict how long you'll live, just as you can't know how well your portfolio would do over time. But a new generation of calculators will compute the odds that your mix of stocks, bonds and cash will support your desired standard of living during retirement. These Monte Carlo simulations work out the probability by running thousands upon thousands of results including worst case scenarios. The best known is offered by financialengines.com. So let's go to financialengines – one word --.com. And from the home page, put our cursor on my info. The advice costs money, but you can get a free forecast and see if you like the service and whether you like looking at the world through the lens of probabilities rather than certainties. Don't forget your Social Security benefits. The Social Security Administration's website is rich with information. So let's go to ssa.gov/retire. And if you look over here, you can calculate your retirement benefits learn about eligibility issues, study your options as retirement nears, and...
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...question that VAR answers. You can see how the "VAR question" has three elements: a relatively high level of confidence (typically either 95% or 99%), a time period (a day, a month or a year) and an estimate of investment loss (expressed either in dollar or percentage terms). Methods of Calculating VAR Institutional investors use VAR to evaluate portfolio risk, but in this introduction we will use it to evaluate the risk of a single index that trades like a stock: the Nasdaq 100 Index, which trades under the ticker QQQQ. The QQQQ is a very popular index of the largest non-financial stocks that trade on the Nasdaq exchange. There are three methods of calculating VAR: the historical method, the variance-covariance method and the Monte Carlo...
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...A SYSTEM SIMULATION STUDY ON THE THREE FAST MOVING PRODUCTS (MARLBORO, C2, VIVA) OF THE COLLEGE VARIETY SHOPPE USING THE MONTE CARLO SIMULATION IN INVENTORY MANAGEMENT EXECUTIVE SUMMARY This study shows how the selected three fast moving products (Marlboro cigarettes, C2, Viva mineral water) move from the current Inventory Management technique of the College Variety Shoppe from its distributors to its warehouse storage to the end user or customer. An excel program and a simulation model was made to observed its current performance. After the observation, the group performs an experimentation that will improve the current technique of the College Variety Shoppe. After simulating the experimentation, the group then give conclusions and recommendations on how to improve the College Variety Shoppe’s current Inventory Management. TABLE OF CONTENTS Title Page ........................................................ 1 Executive Summary ........................................................ 2 Table of Contents ........................................................ 3 Introduction ........................................................ 4 Methodology ........................................................ 6 Model Development ........................................................ 7 Model Validation ........................................................ 11 Experimentation, Results .......
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...Derivative Securities Tutorial Questions Option pricing using Simulation Techniques QUESTION 1 This question refers to the VBA program “Monte Carlo European Option.xlsm” as well as the option discussed in lectures (details repeated as follows) Stock price is currently traded at $1.76. Calculate the price of a European call (strike $1.60, maturity 3 months) on one share. Assume risk free rate of 10% p.a., stock price volatility is 30% p.a. and company not expected to pay any dividends over the next 3 months a) Briefly explain the methodology used to value the European call and put. b) Explain how you would modify the code to price an Asian option. c) Approximate the rho by changing the risk free rate to 9%. Compare this to that from the BSM model where [pic]. d) Now assume a dividend yield of 2% p.a payable over the life of the option. Re-price the option (with risk free rate at 10%). Is the price consistent with your expectations? Why/why not? e) Describe how you could modify the code to allow for leptokurtosis (fat tails). QUESTION 2 Describe how you could use a simulation to price an option using the binomial tree approach. QUESTION 3 Describe the difference between a bootstrap and a monte carlo simulation. Discuss one advantage and disadvantage of the monte carlo approach. QUESTION 4 A Public–private partnership (PPP) describes a government service or private business venture which is funded and operated...
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...When the EB method is used in complex models with many parameters, it often requires the computation of multidimensional definite integrals. This requirement has effectively placed practical limits on the complexity of the problems a long time in the past. However, the parallel development of a Monte Carlo simulation based numerical strategies have revolutionized the applied Bayesian data analysis with the availability of super computing power over the past number of decades. These strategies provide a structure within which many complex Bayesian models can be analyzed using generic software. Moreover, the simulation study is a tractable practice that can be utilized to examine and compare the performance of different estimators empirically. In this study, one generates a sample of random data in such a way that mimics a real problem and recapitulates...
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...quality to be released to the customer, or should be sentenced for scrap or rework due to poor quality. In this case, the batch is the population. Although the population of interest often consists of physical objects, sometimes we need to sample over time, space, or some combination of these dimensions. For instance, an investigation of supermarket staffing could examine checkout line length at various times, or a study on endangered penguins might aim to understand their usage of various hunting grounds over time. For the time dimension, the focus may be on periods or discrete occasions. In other cases, our 'population' may be even less tangible. For example, Joseph Jagger studied the behaviour of roulette wheels at a casino in Monte Carlo, and used this to identify a biased wheel. In this case, the 'population' Jagger wanted to investigate was the overall behaviour of the wheel (i.e. the probability distribution of its results over infinitely many trials), while his 'sample' was formed from observed results from that wheel. Similar considerations arise when taking repeated measurements of some physical characteristic such as the electrical conductivity of copper. This situation often arises when we seek...
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...CFSR/CPR before or after the weekend? 2. D1522 Travel; Does this need to be EV? 3. Monte Carlo every quarter; is this SEAKR requirement or will Customer be handling this? 4. The SDRL document indicated that our deliverables are due 10 working days after accounting month close (not calendar days) 5. For EV methods, can we use 50/50 or are more appropriate X/Y EV needed. 1. If the 15th falls on the weekend, do we need to turn in the CFSR/CPR before or after the weekend? 2. D1522 Travel; Does this need to be EV? 3. Monte Carlo every quarter; is this SEAKR requirement or will Customer be handling this? 4. The SDRL document indicated that our deliverables are due 10 working days after accounting month close (not calendar days) 5. For EV methods, can we use 50/50 or are more appropriate X/Y EV needed. 1. If the 15th falls on the weekend, do we need to turn in the CFSR/CPR before or after the weekend? 2. D1522 Travel; Does this need to be EV? 3. Monte Carlo every quarter; is this SEAKR requirement or will Customer be handling this? 4. The SDRL document indicated that our deliverables are due 10 working days after accounting month close (not calendar days) 5. For EV methods, can we use 50/50 or are more appropriate X/Y EV needed. 1. If the 15th falls on the weekend, do we need to turn in the CFSR/CPR before or after the weekend? 2. D1522 Travel; Does this need to be EV? 3. Monte Carlo every quarter; is this SEAKR requirement or will Customer be handling this? 4. The SDRL...
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...“What Happened to the Monte-Carlo?” Ruth Grey ENC 1101 – Composition 1 February 10, 2010 What Happened to the Monte-Carlo? It was a sunny; warmth summer day, the sky was baby blue with the features of creamy white soft clouds. With the cool breeze blowing softly, the day was innocently inviting, so I went out for a ride. Father and dominant brothers were in the drive-way, worked strenuously on father’s broken red truck. “Oh shoot! What am I going to do now?” I silently questioned myself with one eyebrow slightly upwards. “How am I going to get to the Monte Carlo.?” I kept talking to myself as I tried to think of some tactic, to get pass father and brothers, to get to the monte carlo, parked on the street. “Where do you think, you’re going young lady?” My father asked as I was too focused on getting into the shining brown Monte Carlo. “Ahhhh! I’m getting Mama some ice cream.” The voice belonged to me as I hopped into the interior of the Monte carol and made my way to the store. That day, I was going north on Atlantic Ave in Long Beach, through a heavy street traffic. With music blasting as I yelled sang my lungs out, it was another typical short ride to the store. To ignore the fear of my father’s voice, when I cruised off the house, I went fast, too fast passing numerous cars, despite of the busy traffic as I drove down on Atlantic Ave towards my destination. One quick second, that’s all it takes for everything to go right or wrong. My dark brown eyes opened...
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...Writing and healing Stacy Marvin My life When I think back on the life I have had, no one can take my memories away. The time I had in Florida with my soul mate, my best friend was irreplaceable to me. I cannot even explain how much I have learned from my life, the good and the bad. I want to share something with you from my past but also more recent. Here is one of my childhood memories along with one of the most heartbreaking ones that only happened on June 11, 2013. The sound of the engine revving up as I hit ninety around the twists and turns of the curvy road was the best adrenaline rush I ever had in my life. I was eleven years old and driving my dad’s brand new SS Monte Carlo. Heading to pick up my best friend Debbie. The roads were wet with the rain from earlier on that day. I turned down this dead end road and we started jamming to the music we cranked up a few minutes earlier. We did not see the curve in the road and I lost control of the car and ended up off an embankment that went down to the old railroad tracks. This cliff as I call it, used to have trains running through it, but then was just a rock quarry. Debbie and I both screamed as we skidded and lost control of the car and everything went silent. We were hanging off the edge, afraid to move. We just knew this was it for us, we told each other the final words we thought we would ever hear,( I love you my friend, you mean the world to me, I am glad you are here with me and she said the...
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...Narrative Writing Car accidents Lisa Daniels Everest University Car accidents happen every day to innocent people, yet they are the victims. I think if everyone slowed down and cut out the distractions, pay attention to the road maybe less accidents would occur. I was in a really bad car accident when I was 17. It was a late night and I was heading to pick up and friend. I was driving a 1978 Monte Carlo. I was making a left hand turn, as I was doing so the light changed to red, and the guy that was heading towards me ran that light and hit me on the passenger side door. My left side of my head hit the driver’s side window, all of the impact from him hitting me jotted me out the passenger window, my car was on one side of the road on the side walk and I lying on the opposite side of the road on the sidewalk. Angel’s must have been with me that night. I was in a coma; my forehead was stitched up with 150 stitches. The first voice I heard was my mom’s asking how I was doing, I then heard the doctor tell my mom I may not make it. I was so happy to see my mom! I didn’t know who I was, where I was, or what happened to me but I recognized my mom right away. I am blessed to be alive!! I have been in 6 car accidents, but I only caused one. Remembering to pay attention to your surroundings and cutting out distractions while driving, turning the music down to hear the ambulance and police will help you to concentrate on the road. Phone calls, texts, yelling in the car...
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...Beautiful Object Has it ever occurred to you that a car can resemble beauty like a person in many ways? Well I have, the day I first saw my friend’s car. I was leaving school early one day and as I walked closer to the path leading to the street a huge gleam shot across my face. When I turned and looked, there it was, one of the most beautiful objects I’d ever seen parked across the street. It was my friend in his new white Monte Carlo. The paint job on the car reminded me of that cup of milk before I dunk my cookies in it. The car sat high, and on it were the beautiful 22 inch chrome rims. Upon entering the car I noticed that it was elegant and detailed. The car was white like a full moon at night, just as smooth and glossy. The windows were tinted black like the hair of a goddess. The way the car looked at me with a grin, and the front looked mean just like how my little brother looks when I do something he doesn’t like. The curves on the car reminded me of the muscles of a body builder except this muscle had four wheels. Monte Carlo is a well known car maker and all their cars are breath taking but what made this car so different was the accessories that my friend had put on it. The rims were the right size and the chrome color complemented the car just the right way. When I entered the car, the smell of a new car took over me. It was the smell of the leather inside the car mixed with the jasmine scented air freshener. My friend also had televisions put in car that...
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