# A Time Series Analysis of the Adjusted Closing Stock Prices

Topics: Put option, Call option, Option Pages: 9 (2192 words) Published: March 22, 2013

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 "to organize the world's information and make it universally accessible and useful”, and the company's unofficial slogan is "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–Scholes 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. lt 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. An 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 “call”& “put “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| 0.475| 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|...