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...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 the notification) q = 0.028 (Dividend payment= $0.57/share...

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...Supervisor: PETER LØCHTE JØRGENSEN Author: QIAN Zhang (402847) Pricing of principle protected notes embedded with Asian options in Denmark ---- Using a Monte Carlo Method with stochastic volatility (the Heston Model) Aarhus School of Business and Social Science 2011 2 Acknowledgements My gratitude and appreciation goes to my supervisor Peter Lø chte Jø rgensen, for his kind and insightful discussion and guide through my process of writing. I was always impressed by his wisdom, openness and patience whenever I wrote an email or came by to his office with some confusion and difficulty. Especially on access to the information on certain Danish structured products, I have gained great help and support from him. 3 Abstract My interest came after the reading of the thesis proposal on strucured products written by Henrik, as is pointed out and suggested at the last part of this proposal, one of the main limitations of this thesis may be the choice of model. This intrigues my curiosity on pricing Asian options under assumption of stochstic volatility. At first, after the general introduction of strucutred products, the Black Scholes Model and risk neutral pricing has been explained. The following comes the disadvanges of BS model and then moves to the stochastic volatility model, among which the Heston model is highlighted and elaborated. The next part of this thesis is an emricical studying of two structured products embbeded with Asian options in Danish......

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...Exploiting Volatility In the times of recession and variability with the market getting volatile with very far glimpse of normalcy being stored, it would not be a good suggestion to just sit and watch rather it would be a better strategy to make ways to scale up the investment by learning to exploit volatility by diversifying asset allocation, rebalancing portfolio and option strategies. High return volatility definitely increases the fluctuation of the asset class weightings around the target allocation and increases the risk of significant deviation from the target but greater volatility also results in compounded returns . It is substantiated by the situation when the government is spending trillions of dollars to stimulate the growth in the economy and the corporate world is moving ahead with aggressive restructuring. Volatility can be exploited by diversifying the portfolio with bonds as bonds and equities are well correlated and the bonds in the portfolio also dramatically reduces the risk during financial crises. There would be loss but by a lower percentage than in the situation of all equity or lower bond ratio portfolios. The second situation is to avoid risk of market concentration when there is subsequent rise in equity market and then sudden collapse. For this systematic rebalancing is very advantageous as it reduces the downside risk by reducing volatility and investors increase long term portfolio performance by creating alpha and reducing risk. This......

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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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...MEASURING TIME VARYING VOLATILITY OF USDINR CURRENCY FUTURES IN INDIA *Suhashini.J ** Dr.Chandrasekar.K *Suhashini.J, Faculty Research Scholar, PSNA College of Engineering and Technology, Dindigul, Tamilnadu.Suhashinij@gmail.com **Dr.K.Chandrasekar, Assistant Professor, Alagappa Institute of Management, Alagappa University, Kariakudi. MEASURING TIME VARYING VOLATILITY OF USDINR CURRENCY FUTURES IN INDIA Abstract This paper examines the volatility of USDINR currency pair. USDINR currency pair was introduced in regulated stock exchange of National Stock Exchange in the year 2008. USDINR currency stated to trade as a future instrument on 29.08.2008. Though it’s a delayed decision undertaken in India to introduce currency futures in regulated exchange within the three years of its introduction 10 times of volume traded has increased. The pricing of currencies is supposed to be dependent on volatility of the markets. Therefore it’s important to know the volatility implications of currency market to trade in futures market. To understand volatility implications it is examined using ARCH, GARCH, and GARCH (1, 1) model in this paper. The study finds the evidence of time varying volatility of futures. The study finds an evidence of time varying volatility, which exhibits clustering, high persistence and predictability of currency futures in Indian Market. Key words: Time Varying Volatility, currency futures, USDINR and GARCH Introduction Currency Futures has......

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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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...One of the disclosed pitfalls of TrueCrypt disk encryption is that the master keys must remain in RAM in order to provide fully transparent encryption. In other words, if master keys were allowed to be flushed to disk, the design would suffer in terms of security (writing plain-text keys to more permanent storage) and performance. This is a risk that suspects have to live with, and one that law enforcement and government investigators can capitalize on. The default encryption scheme is AES in XTS mode. In XTS mode, primary and secondary 256-bit keys are concatenated together to form one 512-bit (64 bytes) master key. An advantage you gain right off the bat is that patterns in AES keys can be distinguished from other seemingly random blocks of data. This is how tools like aeskeyfind and bulk_extractor locate the keys in memory dumps, packet captures, etc. In most cases, extracting the keys from RAM is as easy as this: $ ./aeskeyfind Win8SP0x86.raw f12bffe602366806d453b3b290f89429 e6f5e6511496b3db550cc4a00a4bdb1b 4d81111573a789169fce790f4f13a7bd a2cde593dd1023d89851049b8474b9a0 269493cfc103ee4ac7cb4dea937abb9b 4d81111573a789169fce790f4f13a7bd 4d81111573a789169fce790f4f13a7bd 269493cfc103ee4ac7cb4dea937abb9b 4d81111573a789169fce790f4f13a7bd 0f2eb916e673c76b359a932ef2b81a4b 7a9df9a5589f1d85fb2dfc62471764ef47d00f35890f1884d87c3a10d9eb5bf4 e786793c9da3574f63965803a909b8ef40b140b43be062850d5bb95d75273e41 Keyfind progress: 100% Several keys were identified, but......

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...Introduction When the stock market goes up one day, and then goes down for the next five, then up again, and then down again, that’s what you call market volatility. Historically, the volatility of the stock market is roughly 20% a year and 5.8% a month, but volatility keeps on changing, so we go through periods of high volatility and low volatility. Analysts and experts have different opinions about what you should do in volatile markets, and how to scope with stock market volatility or the tendency for share prices rising and falling. Analysts. Justin Stewart, co-founder of Seven Investment Management says: “ Crashes happen. If you are a longer-term investor, you should look straight through them and remember the power of compounding dividends, or in cone arising on income.” Andrew Humphries, a director of St James Place Wealth Management, thinks that Diversification is very important and having a portfolio that is solely exposed to one asset class- be it equities, bond or property- is dangerous and all investors should ensure they hold an appropriate range of assets” Andrew Bell, the chief executive of Witan Investment trust advised: “ It is better to buy into fear and cheapness and sell into euphoria and high valuation, as long as you can endure the period before trends reverse. Investors should have this tattooed somewhere to prevent natural human psychology from making them do the opposite. Bill Mott, the manager of PSigma income, said “ in an uncertain world,......

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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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...Ibrahim Nasser Khatatbeh May, 2013 Q1: Explain how the option pricing formula developed by black and scholes can be used for common stock and bond valuation. Include in your discussion the consequences of using variance applied over the option instead of actual variance. Its generally known that Black and Scholes model became a standard in option pricing 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......

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...Market Volatility: Measures and Results Gary E. Mullins, Ph.D. University of Wisconsin - Stevens Point | | IntroductionVirtually everyone who is interested in financial markets seems to agree on two things: that markets are now more volatile than ever, and that volatility causes many problems. Let's look at some recent and not-so-recent articles concerning volatility. This week turned out to be slower than expected on the IPO market, as intense volatility on U.S. exchanges prompted many companies to put off much-anticipated debuts. I am writing to you today to address my concerns about trading in a fast market, a current issue of extreme importance to me. I want to give you my perspective and let you know the steps we at Schwab are taking to support investors during this time of market volatility. In recent months, there has been a marked increase in price volatility and volume in many stocks, particularly of companies that sell products or services via the Internet (Internet issuers). In the above quotes, there are two implicit assumptions: that volatility is higher now than it has been in the past, and that this volatility is somehow bad. In the first article, it assumes that (obviously) increased volatility has caused firms to delay their Initial Public Offerings (IPO's). Next, Schwab believes that investors need special support because of the high volatility inherent in today's market. Finally, Barrett appears to be more concerned about volatility......

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...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 published in his doctoral thesis at 1900. His “theory of speculation” (Theorie de la Speculation, see Bachelier(1900)) was discounted by none other than Henri Poincare, observing that “Mr. Bachelier has evidenced an original and precise mind......

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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......

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...(2002) 45–60 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......

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...NBER WORKING PAPER SERIES FINANCIAL RISK MEASUREMENT FOR FINANCIAL RISK MANAGEMENT Torben G. Andersen Tim Bollerslev Peter F. Christoffersen Francis X. Diebold Working Paper 18084 http://www.nber.org/papers/w18084 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 May 2012 Forthcoming in Handbook of the Economics of Finance, Volume 2, North Holland, an imprint of Elsevier. For helpful comments we thank Hal Cole and Dongho Song. For research support, Andersen, Bollerslev and Diebold thank the National Science Foundation (U.S.), and Christoffersen thanks the Social Sciences and Humanities Research Council (Canada). We appreciate support from CREATES funded by the Danish National Science Foundation. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER 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...

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