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Guidone 1 Throughout time Shakespeare has influenced society in many ways. He has been a great inspiration to literature, plays, painters, movies and language. Many of his plays and poems have been required as a part of liberal education. His idea’s on such subjects as heroism, romantic love, and the nature of tragedy have shaped the attitudes of millions of people and influenced their thinking.   Ã‚  Ã‚  Ã‚  Ã‚  Shakespeare contributed greatly to the English speaking language. Many phrases and words from Shakespeare’s poems and plays have become apart of our everyday speech. Millions of people that use his words or phrases are unaware they are created by him. Some common words he has invented are assassination, bump, eventful, and disgraceful conduct. Shakespeare introduced almost 3,000 words into the Oxford English Dictionary. There are over 1700 common words of Shakespeare origin in our everyday vocabulary. The most rapid growth of vocabulary in the recorded history of language was the period of Shakespeare. Due to his inventiveness and creative word play he has had the greatest impact on our daily vocabulary. Many people quote Shakespeare almost everyday without knowing it. If a person doesn’t understand my argument and the one party state’s â€Å"It’s Greek to me†, or if someone has ever â€Å"Refused to budge an inch†, they a re quoting excerpts of Shakespeare. Many people re-sight lines from Shakespeare’s plays without even reading them. One of the most famous lines is â€Å"To be or not to be.† He experimented with all sorts of words and phrases to create vivid pictures in the mind. Shakespeare helped shape many English speaking countries. He often invented and changed words around. Some of Shakespeare’s words may be confusing or unfamiliar to Guidone 2 many of the modern readers. However, many of the words he had employed are no longer being used.   Ã‚  Ã‚  Ã‚  Ã‚  Since Shakespeare’s death he has influenced every generation of writers, painters and still has some impact on contemporary plays. Many rhetoric devices were used in his work, that writers are often using now. Some familiar ones are alliteration, which is the same sound being repeated in a line or group of lines and repetition, which is when something repeats itself. He often used a lot of imagery, which many writers found useful. With imagery writers were able to create excitement. Shakespeare’s Macbeth was one of the famous and brilliant examples of imagery. There are many paintings from Macbeth that have been done by some of the best artist.

A Time Series Analysis of the Adjusted Closing Stock Prices

Table of Contents 1. ?Introduction 2. ?literature review 3. ?Introduction 4. ?Methodology INTRODUCTION Google Inc. is an American multinational corporation which provides Internet-related products and services, including Internet search, cloud computing, software and advertising technologies. The company was founded by Larry Page and Sergey Brin while both attended Stanford University. Google was first incorporated as a privately held company on September  4, 1998, and its initial public offering followed on August  19, 2004. The company is now listed on the NASDAQ stock exchange under the ticker symbol .The company's mission statement from the outset was â€Å"to organize the world's information and make it universally accessible and useful†, and the company's unofficial slogan is â€Å"Don’t be evil†. In 2006, the company moved to its current headquarters in Mountain View, California. Objectives 1. To fit a multiple regression model to a data set comprising the put, call and strike prices of a stock belonging to a company listed on a known index. 2. To use the BSM Model to which provides a mathematical science for the pricing and hedging of European Call and Put options as the American Options market 3.We wanted to analyze the data for Google option prices from the S;P index over the past and present time periods in order to be able to forecast the future. Literature Review 1. Put call parity In financial mathematics, put–call parity defines a relationship between the price of a European call option and European put option in a frictionless market —both with the identical strike price and expiry, and the underlying being a liquid asset. In the absence of liquidity, the existence of a forward contract suffices.Put–call parity requires minimal assumptions and thus does not require assumptions such as those of Black–Scholes or other commonly used financial models. 2. Black-Scholes Model The Black–Schole s model or Black–Scholes-Merton is a mathematical model of a financial market containing certain derivative investment instruments. From the model, one can deduce the Black–Scholes formula, which gives the price of European-style options. The formula led to a boom in options trading and legitimized scientifically the activities of the Chicago Board Options Exchange and other options markets around the world. t is widely used by options market participants Methodology The data being analyzed consisted of daily past prices of silver traded on the S;P index since 14th May to 22 September 2012. The group was required to obtain data sets containing put, call and strike prices the data set of option expiring in more than 30 days but less than 100 The data was obtained from marketwatch. com on 14th May 2012 copied to excel and imported to R, with the stock price at $605. 23. The group chose options expiring on 22th September 2012 for the 1st data set, with 94 days to expiry.A n average of the Bid and Ask prices of both the call and put options was then calculated as shown below. The values in the columns labeled â€Å"call†; â€Å"put â€Å"were calculated as an average of the corresponding Bid ; Ask call and put prices respectively. A number of statistical methods were applied to analyze the data on the R program. We first started by importing the data to the R program; below is a table showing the data. Strike | call| put| Strikesq| Adj Close| 295| 311. 75| 0. 45| 87025| 605. 23| 300| 306. 45| 0. 425| 90000| 613. 66| 305| 303. 1| 0. 45| 93025| 609. 15| 310| 297. 6| 0. 75| 96100| 612. 79| 315| 291. 4| 0. 5| 99225| 607. 55| 320| 286. 6| 0. 55| 102400| 596. 97| 325| 282. 75| 0. 6| 105625| 611. 02| 330| 277. 85| 0. 65| 108900| 607. 26| 335| 273. 4| 0. 775| 112225| 604. 43| 340| 266. 6| 0. 7| 115600| 604. 85| 345| 262. 1| 0. 75| 119025| 614. 98| 350| 256. 7| 0. 8| 122500| 615. 47| 355| 253. 3| 0. 875| 126025| 609. 72| 360| 248. 35| 0. 875| 129600| 601. 27| 365| 243. 45| 0. 925| 133225| 597. 6| 370| 237. 35| 1| 136900| 596. 06| 375| 232. 4| 1. 05| 140625| 599. 3| 380| 227. 45| 1. 05| 144400| 607. 45| 385| 222. 55| 1. 2| 148225| 609. 57| 390| 218. 85| 1. 325| 152100| 606. 7| 395| 212. 45| 1. 45| 156025| 624. 6| 400| 207. 9| 1. 525| 160000| 651. 01| 405| 202. 95| 1. 6| 164025| 635. 96| 410| 198. 15| 1. 65| 168100| 626. 86| 415| 193. 15| 1. 825| 172225| 630. 84| 420| 188. 4| 2. 025| 176400| 632. 32| 425| 183. 6| 2. 25| 180625| 635. 15| 430| 180| 2. 375| 184900| 642. 62| 435| 175. 25| 2. 55| 189225| 646. 92| 440| 170. 3| 2. 9| 193600| 641. 24| 445| 164. 6| 3. 025| 198025| 648. 41| 450| 160. 9| 3. 3| 202500| 655. 76| 455| 155. 15| 3. 55| 207025| 647. 02| 460| 150. 6| 3. 85| 211600| 649. 33| 465| 146. 8| 4. 05| 216225| 642. 59| 470| 141. 15| 4. 55| 220900| 646. 05| 75| 137. 65| 4. 95| 225625| 639. 98| 480| 132. 05| 5. 35| 230400| 633. 49| 485| 128. 5| 5. 8| 235225| 633. 98| 490| 123. 45| 6. 2| 240100| 625. 04| 495| 118. 65| 6. 75| 2 45025| 621. 13| 500| 114. 1| 7. 4| 250000| 615. 99| 505| 110. 75| 7. 95| 255025| 617. 78| 510| 105. 65| 8. 5| 260100| 605. 15| 515| 101. 35| 9. 45| 265225| 600. 25| 520| 98| 10. 25| 270400| 607. 14| 525| 93. 15| 11. 1| 275625| 606. 8| 530| 89. 55| 11. 95| 280900| 604. 96| 535| 85. 15| 13. 05| 286225| 614. 25| 540| 80. 6| 14. 15| 291600| 621. 25| 545| 76. 85| 15. 3| 297025| 622. 4| 550| 72. 9| 16. 35| 302500| 618. 25| 555| 69. 5| 17. | 308025| 618. 39| 560| 66. 05| 19. 2| 313600| 609. 31| 565| 62. 8| 20. 75| 319225| 609. 9| 570| 59. 15| 22. 45| 324900| 606. 11| 575| 56. 5| 24. 05| 330625| 607. 94| 580| 52. 75| 26| 336400| 614| 585| 49. 7| 27. 85| 342225| 604. 64| 590| 46. 7| 29. 6| 348100| 606. 52| 595| 43. 9| 31. 9| 354025| 605. 56| 600| 40. 95| 34. 35| 360000| 609. 76| 605| 38. 45| 36. 7| 366025| 612. 2| 610| 36. 1| 38. 85| 372100| 605. 91| 615| 33. 55| 41. 35| 378225| 611. 46| 620| 31. 05| 44. 15| 384400| 609. 85| 625| 29. 5| 46. 9| 390625| 606. 77| 630| 27. 35| 49. 75| 396900| 60 9. 09| 635| 25. 3| 52. 95| 403225| 596. 33| 40| 23. 2| 56| 409600| 585. 11| 645| 21. 6| 59. 2| 416025| 580. 83| 650| 19. 95| 62. 65| 422500| 580. 11| 655| 18. 6| 66. 15| 429025| 577. 69| 660| 16. 85| 70. 1| 435600| 579. 98| 665| 15. 6| 73. 95| 442225| 568. 1| 670| 14. 4| 77. 55| 448900| 569. 49| 675| 13. 3| 81. 35| 455625| 580. 93| 680| 12. 25| 85. 55| 462400| 585. 52| 685| 11. 05| 88. 25| 469225| 585. 99| 690| 10. 05| 93. 4| 476100| 639. 57| 695| 9. 55| 96. 45| 483025| 632. 91| 700| 8. 45| 102. 25| 490000| 628. 58| 705| 7. 75| 105. 25| 497025| 624. 99| 710| 7. 1| 110. 65| 504100| 629. 64| 715| 6. 75| 114. 75| 511225| 625. 96| 720| 5. 95| 119. 5| 518400| 623. 14| 725| 5. 65| 122. 65| 525625| 622. 46| 730| 5. 05| 128. 5| 532900| 650. 02| 735| 4. 55| 131. 95| 540225| 659. 01| 740| 4. 25| 137. 6| 547600| 668. 28| 745| 3. 95| 142. 35| 555025| 665. 41| 750| 3. 5| 147| 562500| 645. 9| 755| 3. 25| 151. 7| 570025| 642. 4| 760| 2. 975| 155. 95| 577600| 639. 7| 765| 2. 725| 161. 4| 585225| 64 0. 25| 770| 2. 525| 166. 45| 592900| 633. 14| 775| 2. 2| 169. 9| 600625| 629. 7| 780| 2. 125| 174. 75| 608400| 625. 82| 785| 1. 975| 180. 55| 616225| 630. 37| 790| 1. 775| 185. 45| 624100| 621. 83| 795| 1. 65| 190. 35| 632025| 625. 96| 800| 1. 525| 195. 15| 640000| 619. 4| 810| 1. 35| 205. 05| 656100| 618. 07| 820| 1. 175| 214. 95| 672400| 625. 63| 830| 0. 975| 224. 75| 688900| 625. 39| 840| 0. 825| 234. 95| 705600| 627. 42| 850| 0. 725| 244| 722500| 616. 05| 860| 0. 65| 254. 25| 739600| 623. 39| 870| 0. 525| 265| 756900| 623. 77| 880| 0. 475| 274. 55| 774400| 625. 65| 890| 0. 425| 284. 6| 792100| 620. 36| 900| 0. 375| 293. 45| 810000| 613. 77| 910| 0. 375| 304. 7| 828100| 599. 39| 920| 0. 3| 314. 45| 846400| 582. 93| 930| 0. 3| 323. 3| 864900| 588. 19| 940| 0. 275| 333. 25| 883600| 563| 950| 0. 25| 343. 25| 902500| 570. 11| 960| 0. 25| 353. 25| 921600| 580| 970| 0. 25| 363. 25| 940900| 580. 94| Fitting a Multiple regression Model From the results shown? 0=605. 997, ? 1=0. 995, ? 2= -0. 9979. The value of the stock at that point in time wasSt=605. 23. If significant, the estimate ? 2 was to be equated to -e-r (T-t) and the value for r equated. In this formula, T-t is the time to expiry of the options (94 days in our case) and r is the interest on a daily basis (short rate), which was then supposed to be annualized. Since all the estimates were significant, ? 2= -0. 9979=-e-r(94) r=-ln0. 997994=2. 236391*10-5 Annualizing r; r=2. 236391*10-5*250=0. 05592275=5. 2275%, which is the risk. The formula call(Ct)= 605. 997+0. 995put(Pt)-0. 9979(Strike(Kt)) was the model we used to derive values of call prices in relation to the multiple regression model. A plot of these call and strike options is shown below; If significant, the estimate ? 2 was to be equated to -e-r (T-t) and the value for r equated. In this formula, T-t is the time to expiry of the options (94 days in our case) and r is the interest on a daily basis (short rate), which was then supposed to be annuali zed. PROCEDURE FOR FITTING Finally we drew a graph of Call against Strike and this was the graph obtained.The code and resulting graph are shown below, GRAPH FOR CALL AGAINST STRIKE BSM MODEL METHODS To fit the BSM Model and generate theoretical call prices, we obtained and truncated historical data from finance. yahoo. com as shown in the column labeled ‘Adj. Close’ The code snapshot below created a function â€Å"BSM73† We then computed the BSM73 by using the given the data, annualized interest rate (r), stock price, strike price and days to maturity generates the theoretical call prices. The proposed model to be fitted to fit the regression model CtSt= ? 0+? 1KSt+? 2K2St+ ? t main purpose is so as to determine the values of ? ,? 1 ; ? 2 Procedure From the results shown, we get ? 0=1. 313950 , ? 1=-1. 959886, ? 2= 0. 001195. The value of the stock at that point in time was St=605. 23. PLOT BSM CALL PRICE (Yt) AGAINST STRIKE PRICES For data analysis conducted fo r September 2012 options with T-t=94 days and r=5. 922%, the proposed model can be used in option pricing. It can be concluded from the analysis that for options with a longer time to expiry and a smaller interest rate, the proposed model prices the options more accurately than the BSM model in the price ranges where most options are traded. TIME SERIES ANALYSISThe theoretical model for a time financial time series data is given by; Xt = Trend + ARMA + GARCH + WN Where WN is the white noise in the data. We assumed that the GARCH component is equal to 0 We proceeded to investigate whether indeed the data at hand had trend in it. We used the following tools in our investigation * Box plots * ACF * Histogram * Plotting the data Time series of the data. Summary of strike price data. Box plots ACF OF GARCH NOISE Code: ;y=log(strike) ; d=diff(y) ; garch=d^2 ; acf(garch,lag=100,main=†ACF of Garch Noise†) Histogram Code: hist(strike,main=†Histogram of ADJ Closing pricesâ⠂¬ )De-trending the data After having confirmed that the data contained linear trend, we proceeded to de-trend the data by; 1. Finding the natural logarithm of the data ;y=log(strike) 2. Differencing the data ;d=diff(y) We confirmed that the data the data was actually stationery at this point by using the following techniques; * Finding the ACF of the de-trended data and Plotting the de-trended data FIT ARMA (p, q) We found that an ARIMA (2, 2, 0) was the best model for our data FORECASTING We used the ARIMA (2,2,0) model to predict the adjusted closing share prices for the next 10 days:

Slavery and the U.S. government - 1268 Words

Back in the early to mid-1800s, one of the biggest issues was slave trade and the ownership of slaves. The United States was one of the last countries to still allow slavery and at the time, there was much debate as to whether or not slavery should still be allowed. As many people know, this issue was heavily debated over for many years, and eventually, became one of the sparks that started one of the biggest wars this nation has ever encountered. There was much debate at the time as to how the slave trade should be regulated; the southern states believed that slave trade should be decided by the states themselves, while the northern states believed that slave trade should be under federal regulation. As the debates grew more heated, parties began to form on both sides, and different compromises and legislations were passed in an attempt to help mollify one side or the other. Some of those being popular sovereignty as well as the Missouri Compromise; these attempts, however, were ult imately futile, as the civil war did eventually begin. Many events that occurred during this time were all overseen by the U.S. government in some way, whether it is through Congress or through the Supreme Court, and in these two areas, tensions also rose and people began to take sides. Some of the three biggest names in the government at this time were, Henry Clay, John Calhoun, and Daniel Webster; and all three of these men had ties in the issues and debates that were plaguing the governmentShow MoreRelatedThe Reparations to the Descendents of African American Slaves in the United States788 Words   |  4 PagesUnited States government were to support the reparations to the descendents of African American slaves it would be an admitting of their responsibility. This is an issue that the United States government does not want to bring back to the forefront. 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