Black Scholes Option Pricing Model

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    Black Scholes

    Universidad Iberoamericana Cálculo Vectorial Avanzado “Modelo de Black-Scholes y las Opciones Europeas” Mtra. Teresa Martínez Palacios Luisa Adame Elías México, D.F., a 8 de mayo de 2012. Modelo de Black-Scholes y las Opciones Europeas Resumen La finalidad de este trabajo es entender el Modelo de Black-Scholes-Merton. Este método es el que se utiliza con mayor frecuencia para la valuación de opciones europeas en el mercado de derivados. Para poder comprender

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    Credit Risk Model

    Credit Risk Models: Single Firm Default and Contagion Default Analysis Supervisor: P rof essor Fabrizio Cipollini Student: Marco Gambacciani Academic Year 2009/2010 Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Structural Models 1.1 Terminal Default . . . . . . . . . . . . 1.2 First Passage Models . . . . . . . . . . 1.2.1 The Black and Cox’s Model . . 1.2.2 Longstaff and Schwartz’s Model 1.2.3 Leland and Toft’s Model . . . . 1.2.4 Zhou’s Model . . .

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    Mathematical / Statistical Background for Option Pricing

    follows that       12 12  u   u  1 1 2  e du  2  e 2 du  N      2   hence we obtain  1 t  2 1  1 z2 t  z 2 e dz  e 2 N      as claimed.  e 2  7 Theorem (Key Result for option pricing): Let V ~ log normal  m, s 2  so that the standard deviation of the log of V is s  var  log e V   Then the expectation E  max V  K ,0     is given by the formula E  max V  K ,0    E V   N  d1   K  N  d 2

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    Real Options Analysis Thesis

    Second Order Moment Approach to Real Options Analysis Submitted as a Component of Required Courses for the Award of Bachelor of Engineering (Civil) Honours School of Civil Engineering University of New South Wales Author: Ariel Hersh October 2010 Supervisor: Professor David G. Carmichael     i      ORIGINALITY STATEMENT     ‘I hereby declare that this submission is my own work and to the best of my  knowledge  it  contains  no  materials  previously  published  or  written  by  another 

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    Atlantic Computers Pricing Option

    Individual’s Assignment Atlantic Computer: A Bundle of Pricing Options As Atlantic computer was largest manufacturer of servers and other hi-tech product, Jason Jowers has been assigned the task of developing the pricing structure for the Atlantic Bundle, a unique combination of the TRONN server along with the software tool - Performance Enhancing Server Accelerator – called PESA. The TRONN server has been specifically designed to address the current US market demand. In conjunction with the

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    Uwa Plc and Zombie Analysis (Advance Treasury and Risk Management; Derivatives Hediging; Option; Currency Swap)

    as a share option scheme and found that there is a positive relationship (Bebchuk & Fried, 2004). In this option, employees are given the obligation to buy shares with a certain price (called the strike price) for a certain kind of period usually four years to decide whether exercise the option or not (Black & Scholes, 1973). Sometimes, employees need to wait till the end of the period (called European Options) and sometimes employees can exercise in anytime within the option period (called

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    Accounting for Stock Options

    Accounting for Stock Options http://www.nysscpa.org/printversions/cpaj/2005/805/p30.htm Print Accounting for Stock Options Update on the Continuing Conflict By Nicholas G. Apostolou and D. Larry Crumbley AUGUST 2005 - In December 2004, a decade after bending to Congressional pressure and backing away from requiring the expensing of options on financial statements, FASB issued a revised standard to recognize stock-option compensation as an expense on income statements. Many in Congress may

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    To Critically Compare the Arbitrage Pricing Theory with the Capital Asset Pricing Model

    statistical models have emerged to attempt to scientifically measure the potential returns on an investment. The Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT) are two of such models. The purpose of this essay is to critically compare the Arbitrage Pricing Theory with the Capital Asset Pricing Model as used by fund managers in the United Kingdom. Captial Asset Pricing Model (CAPM) When Sharpe (1964) and Lintner (1965) proposed the Capital Asset Pricing Model (CAPM), it

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    Pricing

    to make relates to pricing its products or services. If consumers or organizational buyers perceive a price to be too high, they may purchase competitive brands or substitute products, leading to a loss of sales and profits for the firm. If the price is too low, sales might increase, but profitability may suffer. Thus, pricing decisions must be given careful consideration when a firm is introducing a new product or planning a short or long- term price change. Price and Pricing defined Price is

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    Option Valuation

    Option Valuation Chapter 21 Intrinsic and Time Value intrinsic value of in-the-money options = the payoff that could be obtained from the immediate exercise of the option for a call option: stock price – exercise price for a put option: exercise price – stock price the intrinsic value for out-the-money or at-themoney options is equal to 0 time value of an option = difference between actual call price and intrinsic value as time approaches expiration date, time value goes to zero 21-2

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    Pricing

    Developing Pricing Strategies and Programs Price is the one element of the marketing mix that produces revenue; the other elements produce costs. Prices are perhaps the easiest element of the marketing program to adjust; product features, channels, and even communications take more time. Price also communicates to the market the company’s intended value positioning of its product or brand. A well-designed and marketed product can command a price premium and reap big profits. But new economic realities

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    Aset Pricing

    ASET PRICING AND FINANCIAL STATEMENT INFORMATION PENDAHULUAN Tujuan investor dalam berinvestasi adalah memaksimalkan return. Return merupakan salah satu faktor yang memotivasi investor berinvestasi dan juga merupakan imbalan atas keberanian investor menanggung resiko atas investasi yang dilakukannya. Investor atau orang-orang yang ingin berinvestasi di bursa saham harus memperhitungkan secara hati-hati keuntungan maksimal yang mungkin akan diterima. Agar dapat memperoleh keuntungan, para

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    Covered Call Options

    covered call options on the resources of the different countries that need the funds. An options strategy is when an investor holds a long position (owns the asset: in our case mineral) in an asset and writes (sells) call options on that same asset in an attempt to generate increased income from the asset. This strategy is often employed when an investor has a short-term neutral view on the asset and for this reason holds the asset long and simultaneously have a short position via the option to generate

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    Black-Scholes Option Pricing Model

    Question: Discuss how an increase in the value of each of the determinants of the option price in the Black-Scholes option pricing model for European options is likely to change the price of a call option. A derivative is a financial instrument that has a value determined by the price of something else, such as options. The crucial idea behind the derivation was to hedge perfectly the option by buying and selling the underlying asset in just the right way and consequently "eliminate risk"

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    Capital Asset Pricing Model

    Name: XXXXXX Ahmed XXXXXX Course: XXXXX (Foundation of Financial Analysis and Investment (A) Course: MSC Finance Std: xxxxxxxxx Introduction Asset pricing models are very useful tools in calculating the risk and their respected return for the investors and they are being widely used by financial analyst. From different theories we can determine the value of assets into three steps i.e., Expected Cash Flow, number of periods and the expected rate of returns. Investors have several questions

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    Credit Risk : Merton Model Limitations

    Evaluate of the Merton Model for credit risk analysis The KMV-Merton model proposed by Robert Merton(1974)is an application of classic option pricing theory and as a logical extension of the Black-Scholes(1973)option pricing framework.Merton’s approach assess the credit risk of a firm by characterizing the firm’s equity as a call option on the underling value of the firm with a strike price equal to the face value of the firm’s debt and a time-to-maturity of T.By put-call parity,the value of the

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    Pricing and Hedging Asian Options

      Pricing and Hedging Asian Options By Vineet B. Lakhlani   Pricing  and  Hedging  Asian  Options     Table of Contents   Table of Contents 1. Introduction to Derivatives 2. Exotic Options 2.1.  Introduction  to  Asian  Options   3.1. Binomial Option Pricing Model 3.2. Black-Scholes Model 3.2.1. Black-Scholes PDE Derivation 3.2.2. Black-Scholes Formula 1 2 3 4 4 5 6 7 3   3. Option Pricing Methodologies 4. Asian Option Pricing

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    Black-Scholes Option Pricing Model

    Question: Discuss how an increase in the value of each of the determinants of the option price in the Black-Scholes option pricing model for European options is likely to change the price of a call option. A derivative is a financial instrument that has a value determined by the price of something else, such as options. The crucial idea behind the derivation was to hedge perfectly the option by buying and selling the underlying asset in just the right way and consequently "eliminate risk"

    Words: 1490 - Pages: 6

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    Arundel : Options Case

    rights for their entire portfolio of movies the studios are going to produce over the next year.  Arundel should make an offer to buy sequel rights as the average NPV (on a per film basis ) is $5.51 mn (this is the value calculated using real options method). Hence, we should pay a price below $5.51mn. As per informal inquiries made by us, the studios would be tempted to accept the price of $2mn or more and would not even consider a price below $1mn. We propose that we should negotiate

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    The Promise and Peril of Real Options

    academics have made the argument that traditional discounted cash flow models do a poor job of capturing the value of the options embedded in many corporate actions. They have noted that these options need to be not only considered explicitly and valued, but also that the value of these options can be substantial. In fact, many investments and acquisitions that would not be justifiable otherwise will be value enhancing, if the options embedded in them are considered. In this paper, we examine the merits

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    Three Different Methods of Option Pricing

    Three different methods of option pricing The three different methods of option pricing are: The Black-Scholes model, binomial trees and Monte Carlo Simulation. The three different methods of option pricing are: The Black-Scholes model, binomial trees and Monte Carlo Simulation. The three different methods of option pricing are: The Black-Scholes model, binomial trees and Monte Carlo Simulation. The three different methods of option pricing are: The Black-Scholes model, binomial trees and Monte

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    Black Scholes Model

    Valuing Stock Options: The Black-Scholes-Merton Model Chapter 13 Fundamentals of Futures and Options Markets, 8th Ed, Ch 13, Copyright © John C. Hull 2013 1 The Black-Scholes-Merton Random Walk Assumption  Consider a stock whose price is S  In a short period of time of length Dt, the return on the stock (DS/S) is assumed to be normal with:  mean m Dt  standard deviation s Dt  m is the annualized expected return and s is the annualized volatility. Fundamentals of Futures

    Words: 1783 - Pages: 8

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    Lognormal Stock-Price Models

    Making sense of . . . LogNormal stock-price models in Exams MFE/3 and C/4 James W. Daniel Austin Actuarial Seminars http://www.actuarialseminars.com June 26, 2008 c Copyright 2007 by James W. Daniel; reproduction in whole or in part without the express permission of the author is forbidden. Foreword This document briefly describes the ideas behind the use of LogNormal models for stock prices in some of the material for Exams MFE and C of the Society of Actuaries and Exams 3 and 4 of the

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    Real Options Case

    Real options analysis, Spring 2014 Deadline: March 17, 3:30pm, submit your solution via e‐mail to sspinler@whu.edu Filename convention: <last name>.xls 1. Determine the price for a European call by means of the Black – Scholes equation: S_0 = €118, X = €134, T = 1 year, r= 7%, σ= 40%. 2. How does the price in (1) change if, ceteris paribus, a. X increases b. T increases c. r increases d. σ increases. Draw a chart for (a) to (d). 3. For the same values given in (1), determine the option

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    Capital Asset Pricing Model

    essay about the capital asset pricing model… Hello this is an essay about the capital asset pricing model Hello this is an essay about the capital asset pricing model Hello this is an essay about the capital asset pricing model Hello this is an essay about the capital asset pricing model Hello this is an essay about the capital asset pricing model Hello this is an essay about the capital asset pricing model Hello this is an essay about the capital asset pricing model Hello this is an essay about the

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    Capital Asset Pricing Model Case Study

    Capital Asset Pricing Model Case Study Beta Management Company (HBS Case 9-292-122) We are asked to read the Harvard Case and answer the following questions. The answers need to be clear so I can research your work myself to gain a better understanding. Therefore, please make sure I can follow your reasoning – ie: please provide an explanation behind each of your approaches to answer each question. I intend to use your feedback as the basis to gain a better understanding of this course, which

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    Black Scholes Valuation of Microsoft Employee Stock Options April 2000

    Stock Options, we started by examining the value by using the Black-Scholes Valuation method. We were given that the time period would be T=6 years, and that both the strike price (K) and the Stock Price (S0) were equal to 66.625. When examining the case provided, it gave the data for both volatility and the risk-free rate in 2000. The volatility for this case in 2000 was 0.33 and the risk-free rate was 6.20%. Next, we calculated d1 and d2 in order to evaluate the price of the call option. D1 and

    Words: 1595 - Pages: 7

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    Options

    usually a sign of short-term uncertainty and puts are often purchased as “insurance” on stocks. What’s more, it’s the least risky. QUESTION 3 If you owned AT&amp;T stock, but were concerned about the possibility of bad news. How might you use options to protect yourself against the risk of a price decline? How might you “subsidize” some or all of the cost of protection? Comment on the risks of your chosen “subsidy” strategy. 1) If we are concerned about the possibility of bad news, to protect

    Words: 1137 - Pages: 5

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    Pricing

    to self-select the right option for themselves, signaling their willingness to pay. As a result, this strategy not only incentivizes customers who can go to the movie on weekdays to attend lower-demanded shows, but also extracts more revenue from customers who are only able to attend popular timeslots. Example: Ticket of Interest Mon-Thu Fri Weekend and Public Holidays Before 6pm After 6pm 2D Annabelle GV Plaza $8.50 $9.50 $12.50 $12.50 c) Benefit-based Pricing i) Cinema Versioning: Currently

    Words: 496 - Pages: 2

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    Real Options

    Real Options in Corporate Finance Ellen Bjarnadóttir Thesis of 30 ECTS credits Master of Science in Financial Engineering June 2013 i Real Options in Corporate Finance (Notkun Raunvilnana við töku Fjárfestingaákvarðana) Ellen Bjarnadóttir Thesis of 30 ECTS credits submitted to the School of Science and Engineering at Reykjavík University in partial fulfillment of the requirements for the degree of Master of Science in Financial Engineering June 2013 Supervisor: Dr.Sverrir Ólafsson

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    Atlantic Computer: a Bundle of Pricing Options

    Atlantic Computer: A Bundle of Pricing Options 1. Determine the price for two Tronn servers plus PESA according to the following pricing methods: * Status-quo pricing * Competition-based pricing * Cost-plus Pricing (Hint: footnote # 5) Note: Jowers makes a conservative estimate that two Tronn servers plus PESA equals the performance of four Ontario Zink servers. To calculate the prices you could use the spreadsheet file included in the course content (Week 3). 2

    Words: 566 - Pages: 3

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    Options Study Guide

    Ch 9 Profit profile Pay off profile Definitions know concepts Margin question- how your margin account behaves given certain prices (options) Ch. 10 Variables of option pricing slide 3 –input paramaters affecting stokc options Boundary counditions (eg. Lower bound for European calls) Put call parity –replicate by moving everything else in the other side sell most expensive buy least expensive Slide 5 Bull spread/bear spread using calls and puts, e.g. max profit in bull/bear spread

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    Stock Options

    Stock Options Stock options are a privilege given to an employee to purchase shares of company stock. They give the employee the right to buy common stock from the company at an agreed upon price, also known as the “strike price.” If the value of the stock increases above the agreed upon price, the employee gains additional profit, other than their compensation, from the sale of the option. The purpose of stock options is to give the holder a certain bind to the company’s success. Stock options

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    Crm Pricing

    PRICING OF A PRODUCT (COCA COLA) Third Semester- Project 1 Submitted by: BACHELOR OF BUSINESS ADMINISTRATION (Working Professional) Department of Business Administration January 2015 Acknowledgement I feel deeply indebted towards people who have guided me in this project. It would have not been possible to make such an extensive report without the help, guidance and inputs from them. Most of my information has been from the net by reading a lot about Pricing of a product in marketing

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    Atlantic Computer: a Bundle of Pricing Options

    Coca Cola y Pepsi tienen una ventaja competitiva sostenible; es decir, una ventaja competitiva que perdura por un espacio de tiempo significativo. Tanto para Coca Cola como para Pepsi, lo que representa una verdadera amenaza, son principalmente las acciones que pueda tomar una de ellas, las que erosionan el modelo de negocios de la competencia (Coca Cola en el caso de Pepsi y viceversa). Para luchar contra ello, una alternativa que se ve conveniente, para el caso de Coca Cola por ejemplo, es inventar

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    Pricing

    Marketing 635 MARKETING ANALYTICS AND PRICING Fall 2015 MW 9:35-10:50 – WCBA 184 Instructor: Office: Office Hours: Office Phone: E-mail: Website: Dr. Yan Liu 220U Wehner Building by appointment 845-2547** yliu@mays.tamu.edu http://elearning.tamu.edu **Outside of the classroom, my preferred method of communication is via e-mail. Please note that I will often use e-mail to communicate with you class information. I will send these messages to your neo email account, so please

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    Aggregate Demand and Supply Models Option Two

    Aggregate Demand and Supply Model Option Two Simona Lewis ECO/372 January 14, 2015 Christopher Dabbs Aggregate Demand and Supply Model Option Two Describe the current state of following economic factors. The Interest Rates. When it comes to the interest rates, there are several things that he or she needs to know, such as long-term and short –term interest rates. The term interest rates are the amounts “that are charged or paid for the utilization of financial assets” (Colander, 2013, p

    Words: 748 - Pages: 3

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    Option Pricing, Interest Rate Risk in U.S

    Option Pricing, Interest Rate Risk in U.S Diana PĂUN &amp; Ramona GOGONCEA (2013). Interest Rate Risk Management and the Use of Derivative Securities. Economia Seria Management. Retrieved from: &lt;http://www.management.ase.ro/reveconomia/2013-2/4.pdf&gt; The study by these two authors aims at demonstrating how derivative financial instruments can be utilized to prudently manage interest rate risk majorly faced by numerous banks and financial institutions as well as enable the efficient application

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    Black-Scholes

    instruments such as options, futures and others have been introduced and more commonly used to manage financial risk for improving decision making in this dynamic competitive environment. Options are defined as securities which one party has the right (no obligation) to buy or sell underlying assets with certain price within a certain/specific period of time (Hull, 2012). The option can be either call (right to buy) or put (right to sell) in the form of American options (exercised any time

    Words: 1927 - Pages: 8

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    Flaws with Black Scholes and Exotic Greeks

    Flaws with Black Scholes & Exotic Greeks Treasury Perspectives Flaws with Black Scholes & Exotic Greeks 1 Flaws with Black Scholes & Exotic Greeks 2 Flaws with Black Scholes & Exotic Greeks Dear Readers:It’s been a difficult and volatile year for companies across the Globe. We have seen numerous risk management policies failures. To name a few... UBS, JPM Morgan, Libor manipulations by European, US and Japanese banks and prominent accounting scandals like Lehman… As rightly

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    Second City Options

    Second City Options (SCO) is a small firm that specializes in option trading. Employing 35 people, SCO is located on LaSalle Street in the Chicago financial district. It is a member firm of the Chicago Board Options Exchange (CBOE), where it trades options on stocks and stock indices. It is also a member firm of the Chicago Mercantile Exchange Group (CME Group), where it trades options on futures and the underlying futures contracts. SCO trades for itself and a number of corporate and individual

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    Second City Options: a Case Study on Index Options

    SECOND CITY OPTIONS: A Case Study on Index Options[1] Don M. Chance and Michael L. Hemler (Version: August 30, 2011) Second City Options (SCO) is a small firm that specializes in option trading. Employing 35 people, SCO is located on LaSalle Street in the Chicago financial district. It is a member firm of the Chicago Board Options Exchange (CBOE), where it trades options on stocks and stock indices. It is also a member firm of the Chicago Mercantile Exchange Group (CME Group), where it

    Words: 2333 - Pages: 10

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    Pricing

    SUMMER 2007 V O L . 4 8 N O. 4 Arvind Sahay How to Reap Higher Profits With Dynamic Pricing Please note that gray areas reflect artwork that has been intentionally removed. The substantive content of the article appears as originally published. REPRINT NUMBER 48415 pricing How to Reap Higher Profits With  Dynamic Pricing S un Microsystems Inc. chairman Scott McNealy forecast that “With recent advances in wireless and information technology, even our cars could

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    Capital Asset Pricing Model

    Capital Asset Pricing Model Introduction One factor model that extends the capital asset pricing model (CAPM), adding size and value factors in addition to market risk factor in CAPM. This model considers the fact that the cost and small-capitalization stocks outperform the market on a regular basis. Including these two additional factors that corrects the model for the outperformance trend, which is thought to make it a better tool for evaluating the effectiveness of a manager. FAMA and French

    Words: 1422 - Pages: 6

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    A Novel Simple but Empirically Consistent Model for Stock Price and Option Pricing

    A Novel Simple but Empirically Consistent Model for Stock Price and Option Pricing HUADONG(HENRY) PANG∗ Quantitative Research, J.P. Morgan Chase & Co. 277 Park Ave., New York, NY, 10017 Third draft, May 16, 2009 Abstract In this paper, we propose a novel simple but empirically very consistent stochastic model for stock price dynamics and option pricing, which not only has the same analyticity as log-normal and Black-Scholes model, but can also capture and explain all the main puzzles and phenomenons

    Words: 7582 - Pages: 31

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    Arbitrage - the Key to Pricing Options

    January 1, 2004 Federal Reserve Bank of Cleveland Arbitrage: The Key to Pricing Options by Ed Nosal and Tan Wang A rbitrage is the act of simultaneously buying and selling assets or commodities in an attempt to exploit a profitable opportunity. Although the idea behind arbitrage is fairly simple, it is quite powerful because the ability to exploit such opportunities is needed for markets to operate efficiently. Arbitrage ensures, for example, that buyers and sellers of foreign

    Words: 3298 - Pages: 14

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    Real Options Valuation

    MIT Sloan School of Management Expected Inflation and the Constant-Growth Valuation Model 66 Michael Bradley, Duke University, and Gregg Jarrell, University of Rochester Single vs. Multiple Discount Rates: How to Limit “Influence Costs” in the Capital Allocation process 79 The Era of Cross-Border M&A: How Current Market Dynamics are Changing the M&A Landscape 84 Transfer pricing for Corporate Treasury in the Multinational Enterprise 97 The Equity Market Risk premium

    Words: 9906 - Pages: 40

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    Option Pricing

    examines the problem of pricing a European call on an asset (Stock) that has a stochastic or variable volatility. Addressing this problem was done by investigating two cases: the first case is to determine the option price when the stochastic volatility is independent of stock price. The second case is to determine the option price when the stochastic volatility is correlated with the stock price. This paper provides a solution in series form for the stochastic volatility option, in addition to a discussion

    Words: 797 - Pages: 4

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    Asian Options

    Seminar Summer Term 2012 Practical Financial Engineering ASIAN OPTIONS By Ahmed Mahmoud Harris Rahim Hudson Joel A Seminar Thesis Submitted to the Faculty of Finance and Economics, University of Ulm in Partial Fulfillment of the Requirement for a Masters Degree in Finance Master of Science University of Ulm Ulm, Germany 5th July 2012 DECLARATION We hereby confirm that the seminar thesis is our own work and that we have used only the stated literature and other means.

    Words: 3645 - Pages: 15

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    Pricing

    Customers The continued assessment of prices on consumers’ part is crucial in deriving their perceived value Reference Prices Price and Perceived Quality Measuring customer value * Company This stresses on the alignment of marketing strategy with pricing strategy Price In arriving at price, the following factors were considered. * Price sensitivity of target segment: Notably within our target segment, they are not price sensitive given the differentiated product and service. * Price flexibility

    Words: 741 - Pages: 3

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