환율의 연속적 파워변동성 분포와 이산적 점프 및 미시적 시장교란 효과의 비모수 추정 = Nonparametric Estimation of Continuous Power Variation Distribution, Discrete Jump and Micro-Market Disturbance in Foreign Exchange Rates

다국어 초록 (Multilingual Abstract)

In recent decade, the volatility has been one of the most important topics in finance and time series econometrics. Most studies adopted the parametric approaches such as ARCH class of the modes and stochastic volatility models. The parametric approaches, however, rely on explicit functional forms which can be misspecified. In recent years a few studies adopt nonparametric approaches which are free from specific functional forms. This paper uses a new nonparametric realized volatility model by summing intraday squared returns to explain the discrete jumps as well as continuous volatility so that realized volatility, bipower volatility, relative jump models are introduced. 2) Thus this paper analyzes the recent realized continuous volatility and discrete jump volatility of US dollar returns against the Euro using the ultra-high frequency five minute returns spanning the period from January 2001 through January 2010 during which volatility was appreciably large and the financial crisis appeared in the U.S. and European countries. As results of basic statistics and the density functions, the realized rate of returns, realized variation and realized bipower variation appear the characteristics of nonnormal distributions as usual in the financial time series which have the fat tails. The realized rate of returns, realized variation and realized bipower variation also have the volatility clustering effects and the significant volatility appeared particularly in years 2004 and 2008-2009. The realized jumps of US dollar returns against the Euro appeared to be distributed around zero according to its density function. This paper also uses several tests such as ARCH test, the variance-ratio tests, the long memory tests and Runs tests to analyze the characteristics of realized rate of returns, realized variation and realized bipower variation of US dollar returns against the Euro. Furthermore, this paper introduces the realized jumps using realized bipower variation and then use several jump statistics to identify whether the observed jumps are significant or not. To calculate the jump statistics, this paper uses the tripower quarticity and quadpower quarticity and then estimates the daily several jump statistics at several different crtical values. The empirical results show that many large jumps appear associated with the news announcements after the financial crisis. Especially before and after years 2004 and 2009, the realized variations had the considerably large and discrete jumps when I obtain the jump statistics using tripower and quadpower quarticity. Thus the jump component is important in explaining US dollar exchange rate versus Euro during this the period from January 2001 through January 2010. In the application to the US dollar exchange rate versus Euro, this paper adopts the jump statistics and jump probabilities using tripower and quadpower quarticity, respectively and then estimates the several jump probabilities at different critical values. The empirical estimates shows that the realized US dollar five minute returns against the Euro have the jump probability that there is at least one significant jump per five or seven days during January 2001 through January 2010 at common critical levels.

참고문헌 (Reference)

1 Bollerslev, T, "Volatility Puzzles : A Simple framework for Gauging Return- Volatility Regressions" 131 : 123-150, 2006

2 Bollerslev, T, "Volatility Asymmetry in High Frequency Data" Duke University 2005

3 Bardorff-Nielsen Ole E, "Variation, Jumps, Market Frictions and High Frequency Data in Financial Econometrics" Nuffield College, Oxford University 2005

4 Gallant, A. R., "Using Daily Range Data to Calibrate Volatility Diffusions and Extract the Forward Integrated Variance" 81 : 617-631, 1999

5 Johannes, M. S, "The Statistical and Economic Role of Jumps in Continuous-Time Interest Rate Models" 59 : 227-260, 2004

6 Huang, X, "The Relative Contribution of Jumps to Total Price Variation" 3 : 456-499, 2005

7 Pan, J., "The Jump-Risk Premia Imolicit in Options : Evidence from an Integrated Time Series Study" 63 : 3-50, 2002

8 Eraker, B, "The Impact of Jumps in Volatility and Returns" 58 : 1269-1300, 2003

9 Fleming, J, "The Economic Value of Volatility Timing using Realized Volatility" 67 : 473-509, 2003

10 Andersen, T. G, "The Distribution of Realized Stock Return Volatility" 61 : 43-76, 2001

11 Andersen, T. G, "The Distribution of Realized Exchange Rate Volatility" 96 : 42-55, 2001

12 Mele, A, "Stochatic Volatility in Financial Markets : Crossing the Bridge to Continuous Time" Kluwer Academic Publishers 2000

13 Shephard, N., "Stochastic Volatility : Selected Readings" Oxford University Press 2005

14 Andersen, T. G, "Some Like it Smooth, and Some Like it Rough : Untangling Continuous and Jump Components in Measuring, Modeling and Forecasting Asset Return Volatility" Working Paper, Duke University 2004

15 Bandi, F. M, "Separating Microstructure Noise from Volatility Working Paper" 2005

16 Andersen, T. G, "Roughing it up : including Jump Components in the Measurement, Modelling and Forecasting of Return Volatility" 89 (89): 701-720, 2007

17 Andreou, E, "Rolling Sample Volatolity Estimators : Some New Theoretical Simulation and Empirical Results" 91 : 61-87, 2002

18 Fornari. F, "Recovering the Probability Density Function of Asset Prices using GARCH as Diffusion Approximations" 8 : 83-109, 2001

19 Martens, M, "Realized Volatility with the Realized Range" 138 : 112-133, 2007

20 Hansen, P. R, "Realized Variance and Market Microstructure Noise, Working Paper" Stanford University 2004

21 Bardorff-Nielsen Ole E, "Power and Bipower Variation with Stochastic Volatility and Jumps" 2 : 1-37, 2004

22 Andersen, T. G, "Parametric and nonparametric Volatility Measurement, in Handbook of Financial Econometrics" North Holland 2002

23 Barucci, E, "On Measuring Volatility and the GARCH Forecastinf Performance" 12 : 183-200, 2002

24 Bardorff-Nielsen Ole E, "Non-Gaussian Ornstein-Uhlenbeck-Based Models and Some of Their Uses in Financial Economics" B63 : 167-241, 2001

25 Taylor, S. J, "Modelling Financial Time Series" John Wiley and Sons 1986

26 Andersen, T. G., "Modeling and Forecasting Realized Volatility" 71 : 579-625, 2003

27 Bandi, F. M, "Microstructure Noise, Realized Variance, and Optimal Sampling, Working Paper" University of Chicago, 2005

28 Andersen, T. G, "Micro Effects of Macro Announcements : Real Time Price Discovery in Foreign Exchange" 93 : 38-62, 2003

29 Bardorff-Nielsen Ole E, "Measuring the Impact of Jumps on Multivariate Price Processed Using Bipower Variation Discussion Paper" Nuffield College, Oxford University, 2004

30 Martens, M, "Measuring and Forecasting S&P Index-Futures Volatility using High- Frequency Data" 22 : 497-518, 2002

31 Comte, F, "Long Memory in Continuous Time Stochastic Volatility Models" 8 : 291-323, 1998

32 Bardorff-Nielsen, "Limit Theorems for Bipower Variation in Financial Econometrics, Working Paper" Nuffield College, Oxford University 2005

33 Bardorff-Nielsen Ole E, "How Accurate is the Asymptotic Approximation to the Distribution of Realized Volatility,” in Identification and Inference for Econometric Models. Essays in Honor of Thomas Rothenberg" Cambridge University Press 2005

34 Deo, R, "Forecasting Realized Volatility using a Long-Memory Stochastic Volatility Model: Estimation, Prediction and Seasonal Adjustment" 131 : 29-58, 2006

35 Andersen, T. G, "Forecasting Financial Market Volatility : Sample Frequency vis-a-vis Forecast Horizon" 6 : 457-477, 1999

36 Bollerslev, T, "Estimating Stochastic Volatility Diffusion using Conditional Moments of Integrated Volatility" 109 : 33-65, 2002

37 Bardorff-Nielsen Ole E, "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation" 4 : 2006

38 Eraker, B, "Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices" 59 : 1367-1403, 2004

39 Andersen, T. G, "Deutschemark-Dollar Volatility : Intraday Activity Patterns, Macroeconomic Announcements, and Longer Run Dependencies" 53 : 219-265, 1998

40 Corsi, F, "Consistent High-Precision Volatility from High-Frequency Data" 30 : 183-204, 2001

41 Goncalves, S, "Bootstrapping Realized Volatility Working Paper" Universite de Motreal, 2005

42 Nelson, D. B, "Asymptotically Optimal Smoothing with ARCH Models" 64 : 561-573, 1996

43 Nelson, D. B, "Asymptotic Filtering Theory for Multivariate ARCH Models" 64 : 561-573, 1996

44 rsen, T. G, "Answering the Skeptics : Yes, Standard Volatility Models Do Provide Accurate Forecasts" 39 : 885-905, 1998

45 Hansen, P. R, "An Unbiased Measure of Realized Variance, Working Paper" Stanford University 2004

46 Andersen, T. G, "An Empirical Investigation of continuous-Time Equity Return Model" 57 : 1047-1091, 2002

47 Chernov, Mikhail, "Alternative Models for Stock Price Dynamics" 116 : 225-257, 2003

48 Clark, Peter K, "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices" 41 : 135-155, 1973

49 Andersen, T. G, "A Semiparametric Framework for Modeling and Forecasting Jumps and Volatility in Speculative Prices, Working Paper" Duke University 2005