...Moniruzzaman bhuiyan ID: Co265MHMH0813 Submitted to S.A. Palan Financial Markets and Investment Analysis PD Limited Financial Markets and Investment Analysis Task 1 question answer Introduction For any economy stock market is the heart, the entire economy depends on this market. Normally what do we understand by market? Market is a place where some people buy and some people sell their goods, same thing happen in stock market. In any country or economy there is few people who have innovative idea and passion to take risk but no money, on the other hand there is few people who have money but don’t have the passion to do something. Stock market is the place where this two type people meet and utilize each other. Tens of millions of people look in to stock market to get a comfortable retirement and central bankers watch it closely as they set monetary policy. (Smith, 2004) Now we will try to answer and explain these 3 question bellow….. The ownership of shares is increasingly in the hands of institutions rather than individuals. Does this matter? Shares around the world are increasingly owned by institutions rather than individual. In the UK, over 80% of all shares are estimated to be owned by institution such as pension funds, unit trusts...
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...Impact of derivative trading on the volatility in the stock market of India -Abhinav Barik Abstract This research paper focuses on the impact the derivative trading has had on the stock market of India. The impact is judged by the change in the volatility after the introduction of the derivative trading. In this paper 5 stocks are taken on which derivative trading was introduced and 4 stocks on which derivative trading was not introduced. The daily closing price of those stocks was taken for two periodspre derivative period and the post derivative period. These were analyzed using GARCH model to find the variance equation and then the GARCH coefficients from this equation were compared using the Wald test to check if the volatility has actually changed. The study suggests that the volatility has decreased for 4 companies, increased for 2 and two other companies did not show any significant change in the volatility. * Keywords: volatility, derivative, correlogram diagram, unit root, GARCH, Wald test *MBA student (2010-12), ICFAI BUSINESS SCHOOL, Hyderabad barik.abhinav@rediffmail.com 1. Introduction Derivative trading was introduced on the individual stocks of the Indian market in the year 2001 by SEBI. This was with a view to decrease the risk taken by the investors and to increase the investment opportunities. Since the derivative market and the spot market are linked so that the risk can be transferred, therefore the investors if want to transfer their risk...
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...University Savar, Dhaka FNB209: Financial Institutions and Markets | Executive Summary Submission of the Report on : Efficiency Analysis and Volatility Effect of Bangladesh Stock Market Submitted by:Sariful Islam(Student ID: 610)Ashfaq-ul- haq oni(Student ID: 621)Jafrin Siddique (Student ID: 1922)Zunaid Hossain (Student ID: 1928)K. M. Zeman Adnan (Student ID: 2128)William Masterson Shah (Student ID: 2129) | Submitted to:Dr. Sheikh Abu TaherLecturer,Department of Finance & BankingJahangirnagar University | August 2, 2012 Term Paper Topic: Efficiency Analysis and Volatility Effect of Bangladesh Stock Market Executive Summary: This paper empirically examines the behavior of stock returns in the Bangladesh stock market namely Dhaka Stock Exchange (DSE), the efficiency of the market in pricing securities and the relationship between stock returns and conditional volatility and the impact of some institution factors such as lock-in, circuit breaker, and caretaker government on volatility, using best known three different daily price indices DSEG, DSI and DS20. The results of autocorrelation function, results of ADF and PP tests and also the results of ARIMA models do not support the hypothesis of weak-form of market efficient of DSE. The results of GARCH (p, q)-M models indicate significant departure from the hypothesis of weak form efficiency; the tendency for returns to exhibit volatility clustering; and a significant positive link between risk and returns...
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...1) Using Excel’s standard deviations function to calculate the variability of the stock returns of California REIT, Brown Group, and the Vanguard Index 500. Standard Deviation Vanguard 500 4.61% California REIT 9.23% Brown Group 8.17% Brown Group and California REIT stock returns both have large variability compared to the Vanguard 500. Brown Groups variability is substantially larger that of the Vanguard 500, and California REIT variability is even larger as it is double that of the Vanguard 500. While both Brown Group, and California REIT are more risky then the Vanguard 500, California REIT is the most risking of all as the variability of the stock return is the largest of the three. 2) To compare the two portfolio options Beta is offering portfolio 1 containing 99% of equity funds invested in Vanguard 500, and 1% in California REIT, and portfolio 2 containing 99% Vanguard 500, and 1% in Brown Group. Using Excel function’s to find standard deviations and Excel functions to find covariance. First we calculated the monthly return of portfoilio1, and portfolio 2. After doing that we used Excel function standard deviation to find the variance of each portfolio. Standard Deviation Portfolio 1 4.57% Portfolio 2 4.61% Looking at the two portfolios it is apparent that the portfolio containing Brown Group is riskier, because it adds more variability to the portfolio. This contradicts the answer in question...
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...for their invaluable direction, patience, and guidance throughout this entire process. Abstract The goal of this paper is to investigate the forecasting ability of the Dynamic Conditional Correlation Generalized Autoregressive Conditional Heteroskedasticity (DCC-GARCH). We estimate the DCC’s forecasting ability relative to unconditional volatility in three equity-based crashes: the S&L Crisis, the Dot-Com Boom/Crash, and the recent Credit Crisis. The assets we use are the S&P 500 index, 10-Year US Treasury bonds, Moody’s A Industrial bonds, and the Dollar/Yen exchange rate. Our results suggest that the choice of asset pair may be a determining factor in the forecasting ability of the DCC-GARCH model. I. Introduction Many of today’s key financial applications, including asset pricing, capital allocation, risk management, and portfolio hedging, are heavily dependent on accurate estimates and well-founded forecasts of asset return volatility and correlation between assets. Although volatility and correlation forecasting are both important, however, existing literature has dealt more closely with the performance of volatility models – only very recently has the issue of correlation estimation and forecasting begun to receive extensive investigation and analysis. The goal of this paper is to extend research that has been undertaken regarding the forecasting ability of one specific correlation model, the Dynamic...
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...methods , with almost everything from corporate liabilities and debt instruments can be viewed as option (except some complicated instruments), we can modify the fundamental formula in order to fit the specifications of the instrument that will be valued. An argument done by Black and Scholes which was based on the past proposition of Miller and Modigliani a well as assuming some ideal conditions, States that value of the firm is a sum of total value of debt plus the total value of common stock. As well as the fact that in the absence of taxes, the value of the firm is independent of its leverage and the change of debt has no effect on the firm value. V = E + Dm V: value of the firm. E: shareholders right (common stock values). Dm: market value of the debt. As the above equation impose that Equity (common stock values) can be viewed as a call option on the firm value (due to the shareholders limited liability and with consideration that firm debt can be represent as a zero-coupon bond), where exercising the option means that equity holders buy the firm at the face value of debt (which is in this case will be the exercise price of the option), on the liquidation date of the bond (maturity). The equity value can be represented as the option on the value of the firm (as the remaining after closing the debt on the expiration date) which is limited by the following boundaries: From the above equation the value of equity at the expiration date will be …. ...
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...price calculated by above models make a consistency with the market? The goals of this team project are the answering that question and reasoning the answer. Part. 1: Preparation 1) Collecting historical data We investigated the stock call options and put options of EXXON Mobil. The historical stock price daily data are for 6 months from November 16, 2011 to May 15, 2012. We assume that U.S. Treasury bill with maturity 3 month is risk-free, and use its yield to maturity as risk-free rate. Data are from Yahoo Finance. 2) Calculating preliminary statistics Using the data, the daily log return was calculated Daily log return = ln (△close pricei+1/close pricei) We assumed that the stock price follows Geometric Brownian Motion with constant mean[pic] and standard deviation[pic]. Therefore, the return of the stock was assumed to be normally distributed with mean [pic] and standard deviation [pic]. So we picked up n-days samples of stock prices and estimated the annualized volatility as follows. Next, we calculated the recent historical volatility. Here, n denotes the number of observations (business day), Si denotes the stock price at the end of the i-th interval (i=0, 1, … , n), [pic] denotes the length of the time interval in years (For daily observations, 1/252(business day)) [pic][pic][pic] [pic] = [pic] Estimated daily volatility S = 0.01042889 Estimated annualized volatility [pic] = 0.1655535 Continuous dividend yield (calculated from...
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...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 arising from empirical stock and option markets which log-normal and Black-Scholes model fail to explain. In addition, this model and its parameters have clear economic interpretations. Large sample empirical calibration and tests are performed and show strong empirical consistency with our model’s assumption and implication. Immediate applications on risk management, equity and option evaluation and trading, etc are also presented. Keywords: Nonlinear model, Random walk, Stock price, Option pricing, Default risk, Realized volatility, Local volatility, Volatility skew, EGARCH. This paper is self-funded and self-motivated. The author is currently working as a quantitative analyst at J.P. Morgan Chase & Co. All errors belong to the author. Email: henry.na.pang@jpmchase.com or hdpang@gmail.com. ∗ 1 Electronic copy available at: http://ssrn.com/abstract=1374688 2 Huadong(Henry) Pang/J.P. Morgan Chase & Co. 1. Introduction The well-known log-normal model for stock price was first proposed by Louis Bachelier (1870-1946) and...
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...Taylor & Francis Group, LLC ISSN: 0747-4938 print/1532-4168 online DOI: 10.1080/07474930701853509 REALIZED VOLATILITY: A REVIEW Michael McAleer1 and Marcelo C. Medeiros2 2 School of Economics and Commerce, University of Western Australia Department of Economics, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, Brasil 1 Downloaded At: 15:53 5 September 2008 This article reviews the exciting and rapidly expanding literature on realized volatility. After presenting a general univariate framework for estimating realized volatilities, a simple discrete time model is presented in order to motivate the main results. A continuous time specification provides the theoretical foundation for the main results in this literature. Cases with and without microstructure noise are considered, and it is shown how microstructure noise can cause severe problems in terms of consistent estimation of the daily realized volatility. Independent and dependent noise processes are examined. The most important methods for providing consistent estimators are presented, and a critical exposition of different techniques is given. The finite sample properties are discussed in comparison with their asymptotic properties. A multivariate model is presented to discuss estimation of the realized covariances. Various issues relating to modelling and forecasting realized volatilities are considered. The main empirical findings using univariate and multivariate methods are summarized. Keywords...
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...INSTITUTE O F PHYSICS PUBLISHING RE S E A R C H PA P E R quant.iop.org Dynamics of implied volatility surfaces Rama Cont1,3 and Jos´ da Fonseca2 e Centre de Math´ matiques Appliqu´ es, Ecole Polytechnique, F-91128 e e Palaiseau, France 2 Ecole Superieure d’Ingenierie Leonard de Vinci, F-92916 Paris La D´ fense, e France E-mail: Rama.Cont@polytechnique.fr and jose.da fonseca@devinci.fr Received 20 September 2001 Published 4 February 2002 Online at stacks.iop.org/Quant/2/45 1 Abstract The prices of index options at a given date are usually represented via the corresponding implied volatility surface, presenting skew/smile features and term structure which several models have attempted to reproduce. However, the implied volatility surface also changes dynamically over time in a way that is not taken into account by current modelling approaches, giving rise to ‘Vega’ risk in option portfolios. Using time series of option prices on the SP500 and FTSE indices, we study the deformation of this surface and show that it may be represented as a randomly fluctuating surface driven by a small number of orthogonal random factors. We identify and interpret the shape of each of these factors, study their dynamics and their correlation with the underlying index. Our approach is based on a Karhunen–Lo` ve e decomposition of the daily variations of implied volatilities obtained from market data. A simple factor model compatible with the empirical observations is proposed. We illustrate...
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...working papers are circulated for discussion and comment purposes. They have not been peerreviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications. © 2012 by Torben G. Andersen, Tim Bollerslev, Peter F. Christoffersen, and Francis X. Diebold. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Financial Risk Measurement for Financial Risk Management Torben G. Andersen, Tim Bollerslev, Peter F. Christoffersen, and Francis X. Diebold NBER Working Paper No. 18084 May 2012 JEL No. C1,G1 ABSTRACT Current practice largely follows restrictive approaches to market risk measurement, such as historical simulation or RiskMetrics. In contrast, we propose flexible methods that exploit recent developments in financial econometrics and are likely to produce more accurate risk assessments, treating both portfolio-level...
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...0.1 = 0.05379/0.1 = 0.5379 N(d1) = 0.70467695 d2 = 0.5379 – 10%*√1 = 0.5379 – 0.1 = 0.4379 N(d2) = 0.66927061 e-rcT = e-0.04879*1 = 0.952381 C0 = 50*0.70467695 – 50*0.952381*0.66927061 = 35.2338475 – 31.8700306 = 3.3638 2. Solve the value of the above one-year American call using CBOE Options Toolbox [pic] 3. Noting the Greek values: How will the call value change for a. 1% change in interest rate [pic] b. $1 increases in the stock price [pic] c. Reduction of one-day in maturity [pic] 4. All options are European and the stock does not pay a dividend. Which option is relatively more expensive? Explain. (Hint: Compute implied volatility). a. S = $50, C (X=$60) =$14 [pic] b. S = $50, C (X=$65) =$10 [pic] Option (a) is relatively more expensive because the higher Implied...
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...The Black–Scholes /ˌblæk ˈʃoʊlz/[1] or Black–Scholes–Merton model 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 a theoretical estimate of the price of European-style options. The formula led to a boom in options trading and legitimised scientifically the activities of the Chicago Board Options Exchange and other options markets around the world.[2] lt is widely used, although often with adjustments and corrections, by options market participants.[3]:751 Many empirical tests have shown that the Black–Scholes price is "fairly close" to the observed prices, although there are well-known discrepancies such as the "option smile".[3]:770–771 The Black–Scholes was first published by Fischer Black and Myron Scholes in their 1973 paper, "The Pricing of Options and Corporate Liabilities", published in the Journal of Political Economy. They derived a stochastic partial differential equation, now called the Black–Scholes equation, which estimates the price of the option over time. The key idea behind the model is to hedge the option by buying and selling the underlying asset in just the right way, and consequently "eliminate risk". This hedge is called delta hedging and is the basis of more complicated hedging strategies such as those engaged in by investment banks and hedge funds. The hedge implies that there is a unique price for the option and this is given by the...
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...01.1. In a plot of the volatility smile, what are each of the axes and how is the function line plotted? Y axis is implied volatility. X axis is strike price (K), K/S, K/Forward, or option delta. The line plots volatility (sigma) that, given an observed market price (c), solves for option price (c) = BSM[S,K, sigma, T,rho,(q)]. There is not an analytical solution, we must iterate (goal-seek) to solve for the volatility that returns a model price equal to observed market price. 01.2. Identify the axes in a plot of the (i) volatility term structure and (ii) volatility surface. (i) Implied volatility versus option term (ii) Three dimensions: implied volatility (Y axis) versus strike or K/S (X axis) versus term (Z axis) 01.3 Which is consistent with the lognormal price distribution (GBM) that underlies classic Black-Scholes Merton: volatility smile or volatility skew? Neither! a horizontal line (Y-axis = implied volatility and X-axis = strike price) is consistent with the lognormal price distribution. A smile (i.e., high implied volatility for OTM puts and calls) implies heavier tails, while a skew (i.e., high implied volatility for ITM call/OTM put and low implied volatility for OTM call/ITM put) implies heavy left tail and light right tail. 01.4 True or false: the implied option volatility smile should be the same for all market participants (traders). False. implied volatility, by definition, is model-dependent. It varies with the model employed. Only...
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...Slow Diffusion of Information and Price Momentum in Stocks: Evidence from Options Markets Zhuo Chen∗ Andrea Lu† September 6, 2014 Abstract This paper investigates the source of price momentum in the equity market using information from options markets. The empirical results provide direct evidence of the gradual information diffusion model in Hong and Stein (1999). Consistent with their theory, we show that a successful identification of stocks’ information diffusion stage helps explain momentum profits. We are able to enhance momentum profits by longing winner stocks with higher growth (and shorting loser stocks with larger drop) in call options implied volatility. Our empirical strategy generates a risk-adjusted alpha of 1.8% per month for a hedged winner-minus-loser portfolio over the 1996–2011 period, during which the simple momentum strategy fails to perform. The results are stronger and clearer if we use call options compared with put options, which are consistent with managers’ tendency to reveal good news and hide bad news. Our results are robust to transaction costs, choice of options’ moneyness, elimination of implied volatility persistence, and choice of options’ time-to-maturity. Finally, our results are not driven by existing stock-level characteristics, such as size, trading volume, and analyst coverage. JEL Classification: G10, G11, G12, G13 Keywords: Momentum, Implied Volatility PBC School of Finance, Tsinghua University. Email: chenzh@pbcsf.tsinghua.edu.cn...
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