Bayesian Estimation of the Markov-Switching GARCH(1,1) Model with Student-t Innovations
|
|
- Jasmine Ellis
- 6 years ago
- Views:
Transcription
1 Bayesian Estimation of the Markov-Switching GARCH(1,1) Model with Student-t Innovations Department of Quantitative Economics, Switzerland R/Rmetrics User and Developer Workshop, Meielisalp, July 2007
2 MOTIVATION Why using MS-GARCH models? High persistence with GARCH models (structural breaks); Markov-switching ARCH [Hamilton and Susmel, 1994]; Markov-switching GARCH [Gray, 1996; Klaassen, 2002; Haas et al., 2004]; Very flexible models. Better volatility forecasts.
3 MOTIVATIONS Why using the Bayesian approach? ML (EM) estimation is difficult (local max); MCMC methods can explore the full posterior; Model discrimination is possible (w.r.t. the number of states); Probabilistic statements.
4 MOTIVATIONS Why using R? Quick and easy coding; C or Fortran implementation to speed up calculations; Use of the coda (or boa) library to check the MCMC output; Nice plots (legend, symbols, etc...);...
5 OUR CONTRIBUTION MCMC scheme for MS-GARCH(1, 1) model of Haas et al. [2004] with Student-t innovations: Model parameters are updated by block; The state variables are updated in a multi-move manner; The degrees of freedom parameter is generated via an efficient rejection technique. Application to real data set. In-sample and out-sample performance analysis.
6 OUTLINE 1 MS-GARCH(1, 1) model 2 Bayesian estimation 3 Application 4 Conclusion
7 MS-GARCH(1, 1) MODEL Conditional variance process Haas et al. [2004] hypothesize K separate GARCH(1, 1) processes for the conditional variance: h k t. = α k 0 + α k 1y 2 t 1 + β k h k t 1 for k = 1,..., K. This formulation has practical and conceptual advantages: Allows to generate the states in a multi-move manner; Interpretation of the variance dynamics in each regime; Theoretical results on single-regime GARCH(1, 1) available.
8 MS-GARCH(1, 1) MODEL Model specification The MS-GARCH(1, 1) model with Student-t innovations may be written as follows: y t = ε t (ϱh st t ) 1/2 ε t iid S(0, 1, ν) ϱ. = ν 2 ν for t = 1,..., T where the latent process {s t } with state space {1,..., K} is assumed to be a stationary, irreducible Markov process with transition matrix P.
9 MS-GARCH(1, 1) MODEL Model specification (cont.) Equivalent specification (via data augmentation) to perform the Bayesian estimation in a convenient manner: y t = ε t (ω t ϱh st t ) 1/2 ε t iid N (0, 1) ω t iid IG ( ν 2, ν 2 ). for t = 1,..., T
10 BAYESIAN ESTIMATION Simulating from the joint posterior Our MCMC sampler can be decomposed as follows: (s 1 s T ) using FFBS P using Gibbs (α0 1 α2 0 αk 0 α1 1 α2 1 αk 1 ) using M-H (β 1 β K ) using M-H (ω 1 ω T ) using Gibbs ν using efficient rejection
11 BAYESIAN ESTIMATION Label switching Likelihood function and the joint prior are invariant to relabeling the states; The joint posterior distribution will also be invariant; Multimodality (K! modes); Need an identification constraint. We use the permutation sampler of Frühwirth-Schnatter [2001].
12 APPLICATION Data set Demeaned daily log-returns of the SMI; Total of observations; The first log-returns are used for the estimation; The remaining data are used in a forecasting performance analysis.
13 APPLICATION Estimation Single-regime and two-state Markov-switching models; Asymmetric GJR(1, 1) specification of Glosten et al. [1993]: h k t ( ). = α0 k + α1i k {yt 1 0} + α2i k {yt 1 <0} y 2 t 1 + β k h k t 1; Joint posterior sample of size
14 APPLICATION Posterior results for the single-regime model High persistence of the conditional variance process; Presence of the leverage effect: P(α 2 > α 1 y) = 0.999; Conditional leptokurtosis; Unconditional variance exists. Posterior mean [1.173,1.189]. Empirical variance
15 APPLICATION Posterior results for the Markov-switching model Presence of leverage effect in both states; Conditional leptokurtosis but posterior mean and median slightly larger than for the single-regime model; Infrequent mixing between states; Posterior mean of the unconditional variance is 0.56 [0.557,0.563] in state 1 and 2.00 [1.992,2.012] in state 2; Posterior mean of the unconditional variance is [1.128,1.139]. Empirical variance
16 APPLICATION Misspecification tests Probability integral transforms [see Diebold et al., 1998]; Test of autocorrelation and autocorrelation of squares; Joint test for zero mean, unit variance, zero skewness, and the absence of excess kurtosis; No evidence of misspecification at the 5% significance level for both models.
17 APPLICATION Deviance information criterion Alternative to AIC and BIC, as well as LR which are not consistent in a Markov-switching context; The DIC consists of two terms: a component that measures the goodness-of-fit and a penalty term for increasing model complexity (effective number of parameters); Smallest DIC is preferred. Model DIC D p D GJR [6769.9,6770.8] [6765.3,6765.8] [4.49,4.93] MS-GJR [6712.6,6713.8] [6793.9,6794.9] [8.49,9.04] [ ]: 95% confidence interval obtained by bootstrap.
18 APPLICATION Model likelihood Estimate the model likelihood for the two models; Bridge sampling of Meng and Wong [1996]. Model ln p(y) GJR (2.644) MS-GJR (3.191) ln p(y): bridge sampling; ( ) numerical standard error ( 100).
19 APPLICATION Forecasting performance analysis We forecast the one-day ahead VaR (backtest); Quantile of interest that corresponds to the probability associated to a certain extreme loss; Compute the predictive VaR by simulation; Test the joint hypothesis of independence and unconditional coverage of the VaR [Christoffersen, 1998].
20 APPLICATION Forecasting performance analysis (cont.) We consider the GJR and MS-GJR models; Also a rolling GJR model: 750 log-returns used to estimate the model; Next 50 log-returns used as a forecasting window; The methodology fulfills the recommendations of the BIS in the use of internal models. Test the models over the out-of-sample observations.
21 APPLICATION Forecasting performance analysis (cont.) MS-GJR and rolling GJR outperform the static GJR model; MS-GJR and rolling GJR perform equally well; However, the MS-GJR model has two advantages: Can anticipate structural breaks in the conditional variance process through the filtering probabilities; MS-GJR needs only to be estimated once. Rolling GJR is merely and ad-hoc approach.
22 CONCLUSION MS-GARCH more flexible than GARCH; Bayesian estimation has many advantages; We provide a new block updating scheme for performing the Bayesian estimation for the MS-GARCH model of Haas et al. [2004] with Student-t innovations; Better in-sample and out-sample performance than single regime GARCH.
23 THE END Thanks for your attention! The working paper is available from: Typeset with LAT E X using the package beamer Copyright 2007 All rights reserved
24 References References REFERENCES Christoffersen PF (1998). Evaluating Interval Forecasts. International Economic Review, 39(4), Symposium on Forecasting and Empirical Methods in Macroeconomics and Finance. Diebold FX, Gunther TA, Tsay AS (1998). Evaluating Density Forecasts with Applications to Financial Risk Management. International Economic Review, 39(4), Dueker MJ (1997). Markov Switching in GARCH Processes and Mean-Reverting Stock-Market Volatility. Journal of Business and Economic Statistics, 15(1), Frühwirth-Schnatter S (2001). Markov Chain Monte Carlo Estimation of Classical and Dynamic Switching and Mixture Models. Journal of the American Statistical Association, 96(453), Glosten LR, Jaganathan R, Runkle DE (1993). On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. Journal of Finance, 48(5), Gray SF (1996). Modeling the Conditional Distribution of Interest Rates as a Regime-Switching Process. Journal of Financial Economics, 42(1), Haas M, Mittnik S, Paolella MS (2004). A New Approach to Markov-Switching GARCH Models. Journal of Financial Econometrics, 2(4), Hamilton JD, Susmel R (1994). Autoregressive Conditional Heteroskedasticity and Changes in Regime. Journal of Econometrics, 64(1 2), Klaassen F (2002). Improving GARCH Volatility Forecasts with Regime-Switching GARCH. Empirical Economics, 27(2), Meng XL, Wong WH (1996). Simulating Ratios of Normalizing Constants via a Simple Identity: a Theoretical Exploration. Statistica Sinica, 6,
25 References References
FORECASTING PERFORMANCE OF MARKOV-SWITCHING GARCH MODELS: A LARGE-SCALE EMPIRICAL STUDY
FORECASTING PERFORMANCE OF MARKOV-SWITCHING GARCH MODELS: A LARGE-SCALE EMPIRICAL STUDY Latest version available on SSRN https://ssrn.com/abstract=2918413 Keven Bluteau Kris Boudt Leopoldo Catania R/Finance
More informationAn Implementation of Markov Regime Switching GARCH Models in Matlab
An Implementation of Markov Regime Switching GARCH Models in Matlab Thomas Chuffart Aix-Marseille University (Aix-Marseille School of Economics), CNRS & EHESS Abstract MSGtool is a MATLAB toolbox which
More informationRegime-dependent Characteristics of KOSPI Return
Communications for Statistical Applications and Methods 014, Vol. 1, No. 6, 501 51 DOI: http://dx.doi.org/10.5351/csam.014.1.6.501 Print ISSN 87-7843 / Online ISSN 383-4757 Regime-dependent Characteristics
More informationCross-Sectional Distribution of GARCH Coefficients across S&P 500 Constituents : Time-Variation over the Period
Cahier de recherche/working Paper 13-13 Cross-Sectional Distribution of GARCH Coefficients across S&P 500 Constituents : Time-Variation over the Period 2000-2012 David Ardia Lennart F. Hoogerheide Mai/May
More informationEstimation of the Markov-switching GARCH model by a Monte Carlo EM algorithm
Estimation of the Markov-switching GARCH model by a Monte Carlo EM algorithm Maciej Augustyniak Fields Institute February 3, 0 Stylized facts of financial data GARCH Regime-switching MS-GARCH Agenda Available
More informationIndian Institute of Management Calcutta. Working Paper Series. WPS No. 797 March Implied Volatility and Predictability of GARCH Models
Indian Institute of Management Calcutta Working Paper Series WPS No. 797 March 2017 Implied Volatility and Predictability of GARCH Models Vivek Rajvanshi Assistant Professor, Indian Institute of Management
More informationThe University of Chicago, Booth School of Business Business 41202, Spring Quarter 2009, Mr. Ruey S. Tsay. Solutions to Final Exam
The University of Chicago, Booth School of Business Business 41202, Spring Quarter 2009, Mr. Ruey S. Tsay Solutions to Final Exam Problem A: (42 pts) Answer briefly the following questions. 1. Questions
More informationBooth School of Business, University of Chicago Business 41202, Spring Quarter 2012, Mr. Ruey S. Tsay. Solutions to Midterm
Booth School of Business, University of Chicago Business 41202, Spring Quarter 2012, Mr. Ruey S. Tsay Solutions to Midterm Problem A: (34 pts) Answer briefly the following questions. Each question has
More informationRelevant parameter changes in structural break models
Relevant parameter changes in structural break models A. Dufays J. Rombouts Forecasting from Complexity April 27 th, 2018 1 Outline Sparse Change-Point models 1. Motivation 2. Model specification Shrinkage
More informationGARCH vs. Traditional Methods of Estimating Value-at-Risk (VaR) of the Philippine Bond Market
GARCH vs. Traditional Methods of Estimating Value-at-Risk (VaR) of the Philippine Bond Market INTRODUCTION Value-at-Risk (VaR) Value-at-Risk (VaR) summarizes the worst loss over a target horizon that
More informationTHE INFORMATION CONTENT OF IMPLIED VOLATILITY IN AGRICULTURAL COMMODITY MARKETS. Pierre Giot 1
THE INFORMATION CONTENT OF IMPLIED VOLATILITY IN AGRICULTURAL COMMODITY MARKETS Pierre Giot 1 May 2002 Abstract In this paper we compare the incremental information content of lagged implied volatility
More informationSelection Criteria in Regime Switching Conditional Volatility Models
Selection Criteria in Regime Switching Conditional Volatility Models Thomas Chuffart To cite this version: Thomas Chuffart. Selection Criteria in Regime Switching Conditional Volatility Models. 2013.
More informationForecasting Volatility movements using Markov Switching Regimes. This paper uses Markov switching models to capture volatility dynamics in exchange
Forecasting Volatility movements using Markov Switching Regimes George S. Parikakis a1, Theodore Syriopoulos b a Piraeus Bank, Corporate Division, 4 Amerikis Street, 10564 Athens Greece bdepartment of
More informationFinancial Econometrics Notes. Kevin Sheppard University of Oxford
Financial Econometrics Notes Kevin Sheppard University of Oxford Monday 15 th January, 2018 2 This version: 22:52, Monday 15 th January, 2018 2018 Kevin Sheppard ii Contents 1 Probability, Random Variables
More informationMEASURING PORTFOLIO RISKS USING CONDITIONAL COPULA-AR-GARCH MODEL
MEASURING PORTFOLIO RISKS USING CONDITIONAL COPULA-AR-GARCH MODEL Isariya Suttakulpiboon MSc in Risk Management and Insurance Georgia State University, 30303 Atlanta, Georgia Email: suttakul.i@gmail.com,
More informationStatistical Inference and Methods
Department of Mathematics Imperial College London d.stephens@imperial.ac.uk http://stats.ma.ic.ac.uk/ das01/ 14th February 2006 Part VII Session 7: Volatility Modelling Session 7: Volatility Modelling
More informationLecture 9: Markov and Regime
Lecture 9: Markov and Regime Switching Models Prof. Massimo Guidolin 20192 Financial Econometrics Spring 2017 Overview Motivation Deterministic vs. Endogeneous, Stochastic Switching Dummy Regressiom Switching
More informationFinancial Econometrics Jeffrey R. Russell. Midterm 2014 Suggested Solutions. TA: B. B. Deng
Financial Econometrics Jeffrey R. Russell Midterm 2014 Suggested Solutions TA: B. B. Deng Unless otherwise stated, e t is iid N(0,s 2 ) 1. (12 points) Consider the three series y1, y2, y3, and y4. Match
More informationGARCH Models for Inflation Volatility in Oman
Rev. Integr. Bus. Econ. Res. Vol 2(2) 1 GARCH Models for Inflation Volatility in Oman Muhammad Idrees Ahmad Department of Mathematics and Statistics, College of Science, Sultan Qaboos Universty, Alkhod,
More informationModeling the Market Risk in the Context of the Basel III Acord
Theoretical and Applied Economics Volume XVIII (2), No. (564), pp. 5-2 Modeling the Market Risk in the Context of the Basel III Acord Nicolae DARDAC Bucharest Academy of Economic Studies nicolae.dardac@fin.ase.ro
More informationVolatility Models and Their Applications
HANDBOOK OF Volatility Models and Their Applications Edited by Luc BAUWENS CHRISTIAN HAFNER SEBASTIEN LAURENT WILEY A John Wiley & Sons, Inc., Publication PREFACE CONTRIBUTORS XVII XIX [JQ VOLATILITY MODELS
More informationMarket Risk Analysis Volume II. Practical Financial Econometrics
Market Risk Analysis Volume II Practical Financial Econometrics Carol Alexander John Wiley & Sons, Ltd List of Figures List of Tables List of Examples Foreword Preface to Volume II xiii xvii xx xxii xxvi
More informationComponents of bull and bear markets: bull corrections and bear rallies
Components of bull and bear markets: bull corrections and bear rallies John M. Maheu 1 Thomas H. McCurdy 2 Yong Song 3 1 Department of Economics, University of Toronto and RCEA 2 Rotman School of Management,
More informationResearch Article The Volatility of the Index of Shanghai Stock Market Research Based on ARCH and Its Extended Forms
Discrete Dynamics in Nature and Society Volume 2009, Article ID 743685, 9 pages doi:10.1155/2009/743685 Research Article The Volatility of the Index of Shanghai Stock Market Research Based on ARCH and
More informationConditional Heteroscedasticity
1 Conditional Heteroscedasticity May 30, 2010 Junhui Qian 1 Introduction ARMA(p,q) models dictate that the conditional mean of a time series depends on past observations of the time series and the past
More informationThe University of Chicago, Booth School of Business Business 41202, Spring Quarter 2017, Mr. Ruey S. Tsay. Solutions to Final Exam
The University of Chicago, Booth School of Business Business 41202, Spring Quarter 2017, Mr. Ruey S. Tsay Solutions to Final Exam Problem A: (40 points) Answer briefly the following questions. 1. Describe
More informationMonetary and Fiscal Policy Switching with Time-Varying Volatilities
Monetary and Fiscal Policy Switching with Time-Varying Volatilities Libo Xu and Apostolos Serletis Department of Economics University of Calgary Calgary, Alberta T2N 1N4 Forthcoming in: Economics Letters
More informationBad Environments, Good Environments: A. Non-Gaussian Asymmetric Volatility Model
Bad Environments, Good Environments: A Non-Gaussian Asymmetric Volatility Model Geert Bekaert Columbia University and the National Bureau of Economic Research Eric Engstrom Board of Governors of the Federal
More informationLecture 8: Markov and Regime
Lecture 8: Markov and Regime Switching Models Prof. Massimo Guidolin 20192 Financial Econometrics Spring 2016 Overview Motivation Deterministic vs. Endogeneous, Stochastic Switching Dummy Regressiom Switching
More informationEmpirical Study of Nikkei 225 Option with the Markov Switching GARCH Model
Empirical Study of Nikkei 225 Option with the Markov Switching GARCH Model Hidetoshi Mitsui and Kiyotaka Satoyoshi September, 2006 abstract This paper estimated the price of Nikkei 225 Option with the
More informationDownside Risk: Implications for Financial Management Robert Engle NYU Stern School of Business Carlos III, May 24,2004
Downside Risk: Implications for Financial Management Robert Engle NYU Stern School of Business Carlos III, May 24,2004 WHAT IS ARCH? Autoregressive Conditional Heteroskedasticity Predictive (conditional)
More informationChapter 4 Level of Volatility in the Indian Stock Market
Chapter 4 Level of Volatility in the Indian Stock Market Measurement of volatility is an important issue in financial econometrics. The main reason for the prominent role that volatility plays in financial
More informationFinancial Times Series. Lecture 6
Financial Times Series Lecture 6 Extensions of the GARCH There are numerous extensions of the GARCH Among the more well known are EGARCH (Nelson 1991) and GJR (Glosten et al 1993) Both models allow for
More informationA market risk model for asymmetric distributed series of return
University of Wollongong Research Online University of Wollongong in Dubai - Papers University of Wollongong in Dubai 2012 A market risk model for asymmetric distributed series of return Kostas Giannopoulos
More informationList of tables List of boxes List of screenshots Preface to the third edition Acknowledgements
Table of List of figures List of tables List of boxes List of screenshots Preface to the third edition Acknowledgements page xii xv xvii xix xxi xxv 1 Introduction 1 1.1 What is econometrics? 2 1.2 Is
More informationFinancial Times Series. Lecture 8
Financial Times Series Lecture 8 Nobel Prize Robert Engle got the Nobel Prize in Economics in 2003 for the ARCH model which he introduced in 1982 It turns out that in many applications there will be many
More informationIntraday Volatility Forecast in Australian Equity Market
20th International Congress on Modelling and Simulation, Adelaide, Australia, 1 6 December 2013 www.mssanz.org.au/modsim2013 Intraday Volatility Forecast in Australian Equity Market Abhay K Singh, David
More informationFINANCIAL ECONOMETRICS AND EMPIRICAL FINANCE MODULE 2
MSc. Finance/CLEFIN 2017/2018 Edition FINANCIAL ECONOMETRICS AND EMPIRICAL FINANCE MODULE 2 Midterm Exam Solutions June 2018 Time Allowed: 1 hour and 15 minutes Please answer all the questions by writing
More informationInternet Appendix for Asymmetry in Stock Comovements: An Entropy Approach
Internet Appendix for Asymmetry in Stock Comovements: An Entropy Approach Lei Jiang Tsinghua University Ke Wu Renmin University of China Guofu Zhou Washington University in St. Louis August 2017 Jiang,
More informationThe Great Moderation Flattens Fat Tails: Disappearing Leptokurtosis
The Great Moderation Flattens Fat Tails: Disappearing Leptokurtosis WenShwo Fang Department of Economics Feng Chia University 100 WenHwa Road, Taichung, TAIWAN Stephen M. Miller* College of Business University
More informationForecasting Volatility of Wind Power Production
Forecasting Volatility of Wind Power Production Zhiwei Shen and Matthias Ritter Department of Agricultural Economics Humboldt-Universität zu Berlin July 18, 2015 Zhiwei Shen Forecasting Volatility of Wind
More informationModel Construction & Forecast Based Portfolio Allocation:
QBUS6830 Financial Time Series and Forecasting Model Construction & Forecast Based Portfolio Allocation: Is Quantitative Method Worth It? Members: Bowei Li (303083) Wenjian Xu (308077237) Xiaoyun Lu (3295347)
More informationARCH and GARCH models
ARCH and GARCH models Fulvio Corsi SNS Pisa 5 Dic 2011 Fulvio Corsi ARCH and () GARCH models SNS Pisa 5 Dic 2011 1 / 21 Asset prices S&P 500 index from 1982 to 2009 1600 1400 1200 1000 800 600 400 200
More informationAmath 546/Econ 589 Univariate GARCH Models: Advanced Topics
Amath 546/Econ 589 Univariate GARCH Models: Advanced Topics Eric Zivot April 29, 2013 Lecture Outline The Leverage Effect Asymmetric GARCH Models Forecasts from Asymmetric GARCH Models GARCH Models with
More informationTechnical Appendix: Policy Uncertainty and Aggregate Fluctuations.
Technical Appendix: Policy Uncertainty and Aggregate Fluctuations. Haroon Mumtaz Paolo Surico July 18, 2017 1 The Gibbs sampling algorithm Prior Distributions and starting values Consider the model to
More informationDYNAMIC ECONOMETRIC MODELS Vol. 8 Nicolaus Copernicus University Toruń Mateusz Pipień Cracow University of Economics
DYNAMIC ECONOMETRIC MODELS Vol. 8 Nicolaus Copernicus University Toruń 2008 Mateusz Pipień Cracow University of Economics On the Use of the Family of Beta Distributions in Testing Tradeoff Between Risk
More informationBayesian analysis of GARCH and stochastic volatility: modeling leverage, jumps and heavy-tails for financial time series
Bayesian analysis of GARCH and stochastic volatility: modeling leverage, jumps and heavy-tails for financial time series Jouchi Nakajima Department of Statistical Science, Duke University, Durham 2775,
More informationFinancial Data Mining Using Flexible ICA-GARCH Models
55 Chapter 11 Financial Data Mining Using Flexible ICA-GARCH Models Philip L.H. Yu The University of Hong Kong, Hong Kong Edmond H.C. Wu The Hong Kong Polytechnic University, Hong Kong W.K. Li The University
More informationForecasting Volatility of USD/MUR Exchange Rate using a GARCH (1,1) model with GED and Student s-t errors
UNIVERSITY OF MAURITIUS RESEARCH JOURNAL Volume 17 2011 University of Mauritius, Réduit, Mauritius Research Week 2009/2010 Forecasting Volatility of USD/MUR Exchange Rate using a GARCH (1,1) model with
More informationVolatility Analysis of Nepalese Stock Market
The Journal of Nepalese Business Studies Vol. V No. 1 Dec. 008 Volatility Analysis of Nepalese Stock Market Surya Bahadur G.C. Abstract Modeling and forecasting volatility of capital markets has been important
More informationEvidence from Large Workers
Workers Compensation Loss Development Tail Evidence from Large Workers Compensation Triangles CAS Spring Meeting May 23-26, 26, 2010 San Diego, CA Schmid, Frank A. (2009) The Workers Compensation Tail
More informationNews Sentiment And States of Stock Return Volatility: Evidence from Long Memory and Discrete Choice Models
20th International Congress on Modelling and Simulation, Adelaide, Australia, 1 6 December 2013 www.mssanz.org.au/modsim2013 News Sentiment And States of Stock Return Volatility: Evidence from Long Memory
More informationBooth School of Business, University of Chicago Business 41202, Spring Quarter 2010, Mr. Ruey S. Tsay. Solutions to Midterm
Booth School of Business, University of Chicago Business 41202, Spring Quarter 2010, Mr. Ruey S. Tsay Solutions to Midterm Problem A: (30 pts) Answer briefly the following questions. Each question has
More informationModeling skewness and kurtosis in Stochastic Volatility Models
Modeling skewness and kurtosis in Stochastic Volatility Models Georgios Tsiotas University of Crete, Department of Economics, GR December 19, 2006 Abstract Stochastic volatility models have been seen as
More informationFinancial Econometrics Jeffrey R. Russell Midterm 2014
Name: Financial Econometrics Jeffrey R. Russell Midterm 2014 You have 2 hours to complete the exam. Use can use a calculator and one side of an 8.5x11 cheat sheet. Try to fit all your work in the space
More informationRegime Switching in the Presence of Endogeneity
ISSN 1440-771X Department of Econometrics and Business Statistics http://business.monash.edu/econometrics-and-businessstatistics/research/publications Regime Switching in the Presence of Endogeneity Tingting
More informationValue-at-Risk forecasting ability of filtered historical simulation for non-normal. GARCH returns. First Draft: February 2010 This Draft: January 2011
Value-at-Risk forecasting ability of filtered historical simulation for non-normal GARCH returns Chris Adcock ( * ) c.j.adcock@sheffield.ac.uk Nelson Areal ( ** ) nareal@eeg.uminho.pt Benilde Oliveira
More informationLecture 5: Univariate Volatility
Lecture 5: Univariate Volatility Modellig, ARCH and GARCH Prof. Massimo Guidolin 20192 Financial Econometrics Spring 2015 Overview Stepwise Distribution Modeling Approach Three Key Facts to Remember Volatility
More informationModelling Regime Specific Stock Volatility Behaviour
Modelling Regime Specific Stock Volatility Behaviour Abstract Any GARCH model with a single volatility state identifies only one mechanism governing the dynamic response of volatility to market shocks,
More informationGARCH Models. Instructor: G. William Schwert
APS 425 Fall 2015 GARCH Models Instructor: G. William Schwert 585-275-2470 schwert@schwert.ssb.rochester.edu Autocorrelated Heteroskedasticity Suppose you have regression residuals Mean = 0, not autocorrelated
More informationThe Time-Varying Effects of Monetary Aggregates on Inflation and Unemployment
経営情報学論集第 23 号 2017.3 The Time-Varying Effects of Monetary Aggregates on Inflation and Unemployment An Application of the Bayesian Vector Autoregression with Time-Varying Parameters and Stochastic Volatility
More informationIs there an Asymmetric Effect of Monetary Policy over Time?
Oesterreichische Nationalbank W o r k i n g P a p e r 4 5 Is there an Asymmetric Effect of Monetary Policy over Time? A B a y e s i a n A n a l y s i s U s i n g A u s t r i a n D a t a Sylvia Kaufmann
More informationMarket Risk Prediction under Long Memory: When VaR is Higher than Expected
Market Risk Prediction under Long Memory: When VaR is Higher than Expected Harald Kinateder Niklas Wagner DekaBank Chair in Finance and Financial Control Passau University 19th International AFIR Colloquium
More informationOnline Appendix to ESTIMATING MUTUAL FUND SKILL: A NEW APPROACH. August 2016
Online Appendix to ESTIMATING MUTUAL FUND SKILL: A NEW APPROACH Angie Andrikogiannopoulou London School of Economics Filippos Papakonstantinou Imperial College London August 26 C. Hierarchical mixture
More informationRegime Dependent Conditional Volatility in the U.S. Equity Market
Regime Dependent Conditional Volatility in the U.S. Equity Market Larry Bauer Faculty of Business Administration, Memorial University of Newfoundland, St. John s, Newfoundland, Canada A1B 3X5 (709) 737-3537
More informationLinda Allen, Jacob Boudoukh and Anthony Saunders, Understanding Market, Credit and Operational Risk: The Value at Risk Approach
P1.T4. Valuation & Risk Models Linda Allen, Jacob Boudoukh and Anthony Saunders, Understanding Market, Credit and Operational Risk: The Value at Risk Approach Bionic Turtle FRM Study Notes Reading 26 By
More informationThe GARCH-GPD in market risks modeling: An empirical exposition on KOSPI
Journal of the Korean Data & Information Science Society 2016, 27(6), 1661 1671 http://dx.doi.org/10.7465/jkdi.2016.27.6.1661 한국데이터정보과학회지 The GARCH-GPD in market risks modeling: An empirical exposition
More informationStochastic Volatility (SV) Models
1 Motivations Stochastic Volatility (SV) Models Jun Yu Some stylised facts about financial asset return distributions: 1. Distribution is leptokurtic 2. Volatility clustering 3. Volatility responds to
More informationVOLATILITY. Time Varying Volatility
VOLATILITY Time Varying Volatility CONDITIONAL VOLATILITY IS THE STANDARD DEVIATION OF the unpredictable part of the series. We define the conditional variance as: 2 2 2 t E yt E yt Ft Ft E t Ft surprise
More informationCourse information FN3142 Quantitative finance
Course information 015 16 FN314 Quantitative finance This course is aimed at students interested in obtaining a thorough grounding in market finance and related empirical methods. Prerequisite If taken
More informationA STUDY ON ROBUST ESTIMATORS FOR GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSCEDASTIC MODELS
A STUDY ON ROBUST ESTIMATORS FOR GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSCEDASTIC MODELS Nazish Noor and Farhat Iqbal * Department of Statistics, University of Balochistan, Quetta. Abstract Financial
More informationA Regime Switching model
Master Degree Project in Finance A Regime Switching model Applied to the OMXS30 and Nikkei 225 indices Ludvig Hjalmarsson Supervisor: Mattias Sundén Master Degree Project No. 2014:92 Graduate School Masters
More informationBayesian estimation of the Gaussian mixture GARCH model
Bayesian estimation of the Gaussian mixture GARCH model María Concepción Ausín, Department of Mathematics, University of A Coruña, 57 A Coruña, Spain. Pedro Galeano, Department of Statistics and Operations
More informationShort-selling constraints and stock-return volatility: empirical evidence from the German stock market
Short-selling constraints and stock-return volatility: empirical evidence from the German stock market Martin Bohl, Gerrit Reher, Bernd Wilfling Westfälische Wilhelms-Universität Münster Contents 1. Introduction
More informationBacktesting value-at-risk: a comparison between filtered bootstrap and historical simulation
Journal of Risk Model Validation Volume /Number, Winter 1/13 (3 1) Backtesting value-at-risk: a comparison between filtered bootstrap and historical simulation Dario Brandolini Symphonia SGR, Via Gramsci
More informationAPPLYING MULTIVARIATE
Swiss Society for Financial Market Research (pp. 201 211) MOMTCHIL POJARLIEV AND WOLFGANG POLASEK APPLYING MULTIVARIATE TIME SERIES FORECASTS FOR ACTIVE PORTFOLIO MANAGEMENT Momtchil Pojarliev, INVESCO
More informationIntroductory Econometrics for Finance
Introductory Econometrics for Finance SECOND EDITION Chris Brooks The ICMA Centre, University of Reading CAMBRIDGE UNIVERSITY PRESS List of figures List of tables List of boxes List of screenshots Preface
More informationDaniel de Almeida and Luiz K. Hotta*
Pesquisa Operacional (2014) 34(2): 237-250 2014 Brazilian Operations Research Society Printed version ISSN 0101-7438 / Online version ISSN 1678-5142 www.scielo.br/pope doi: 10.1590/0101-7438.2014.034.02.0237
More informationCFA Level II - LOS Changes
CFA Level II - LOS Changes 2018-2019 Topic LOS Level II - 2018 (465 LOS) LOS Level II - 2019 (471 LOS) Compared Ethics 1.1.a describe the six components of the Code of Ethics and the seven Standards of
More informationRecent analysis of the leverage effect for the main index on the Warsaw Stock Exchange
Recent analysis of the leverage effect for the main index on the Warsaw Stock Exchange Krzysztof Drachal Abstract In this paper we examine four asymmetric GARCH type models and one (basic) symmetric GARCH
More informationCFA Level II - LOS Changes
CFA Level II - LOS Changes 2017-2018 Ethics Ethics Ethics Ethics Ethics Ethics Ethics Ethics Ethics Topic LOS Level II - 2017 (464 LOS) LOS Level II - 2018 (465 LOS) Compared 1.1.a 1.1.b 1.2.a 1.2.b 1.3.a
More informationPredicting the Success of Volatility Targeting Strategies: Application to Equities and Other Asset Classes
The Voices of Influence iijournals.com Winter 2016 Volume 18 Issue 3 www.iijai.com Predicting the Success of Volatility Targeting Strategies: Application to Equities and Other Asset Classes ROMAIN PERCHET,
More informationEvidence from Large Indemnity and Medical Triangles
2009 Casualty Loss Reserve Seminar Session: Workers Compensation - How Long is the Tail? Evidence from Large Indemnity and Medical Triangles Casualty Loss Reserve Seminar September 14-15, 15, 2009 Chicago,
More informationModelling financial data with stochastic processes
Modelling financial data with stochastic processes Vlad Ardelean, Fabian Tinkl 01.08.2012 Chair of statistics and econometrics FAU Erlangen-Nuremberg Outline Introduction Stochastic processes Volatility
More informationBooth School of Business, University of Chicago Business 41202, Spring Quarter 2014, Mr. Ruey S. Tsay. Solutions to Midterm
Booth School of Business, University of Chicago Business 41202, Spring Quarter 2014, Mr. Ruey S. Tsay Solutions to Midterm Problem A: (30 pts) Answer briefly the following questions. Each question has
More informationThe performance of time-varying volatility and regime switching models in estimating Value-at-Risk
Master Thesis, Spring 2012 Lund University School of Economics and Management The performance of time-varying volatility and regime switching models in estimating Value-at-Risk Authors: Supervisor: Alina
More information12. Conditional heteroscedastic models (ARCH) MA6622, Ernesto Mordecki, CityU, HK, 2006.
12. Conditional heteroscedastic models (ARCH) MA6622, Ernesto Mordecki, CityU, HK, 2006. References for this Lecture: Robert F. Engle. Autoregressive Conditional Heteroscedasticity with Estimates of Variance
More informationBacktesting Trading Book Models
Backtesting Trading Book Models Using Estimates of VaR Expected Shortfall and Realized p-values Alexander J. McNeil 1 1 Heriot-Watt University Edinburgh ETH Risk Day 11 September 2015 AJM (HWU) Backtesting
More informationProperties of financail time series GARCH(p,q) models Risk premium and ARCH-M models Leverage effects and asymmetric GARCH models.
5 III Properties of financail time series GARCH(p,q) models Risk premium and ARCH-M models Leverage effects and asymmetric GARCH models 1 ARCH: Autoregressive Conditional Heteroscedasticity Conditional
More informationUSING HMM APPROACH FOR ASSESSING QUALITY OF VALUE AT RISK ESTIMATION: EVIDENCE FROM PSE LISTED COMPANY
ACTA UNIVERSITATIS AGRICULTURAE ET SILVICULTURAE MENDELIANAE BRUNENSIS Volume 65 174 Number 5, 2017 https://doi.org/10.11118/actaun201765051687 USING HMM APPROACH FOR ASSESSING QUALITY OF VALUE AT RISK
More informationUsing MCMC and particle filters to forecast stochastic volatility and jumps in financial time series
Using MCMC and particle filters to forecast stochastic volatility and jumps in financial time series Ing. Milan Fičura DYME (Dynamical Methods in Economics) University of Economics, Prague 15.6.2016 Outline
More informationMeasuring DAX Market Risk: A Neural Network Volatility Mixture Approach
Measuring DAX Market Risk: A Neural Network Volatility Mixture Approach Kai Bartlmae, Folke A. Rauscher DaimlerChrysler AG, Research and Technology FT3/KL, P. O. Box 2360, D-8903 Ulm, Germany E mail: fkai.bartlmae,
More informationVolatility Clustering of Fine Wine Prices assuming Different Distributions
Volatility Clustering of Fine Wine Prices assuming Different Distributions Cynthia Royal Tori, PhD Valdosta State University Langdale College of Business 1500 N. Patterson Street, Valdosta, GA USA 31698
More informationMarket Risk Analysis Volume I
Market Risk Analysis Volume I Quantitative Methods in Finance Carol Alexander John Wiley & Sons, Ltd List of Figures List of Tables List of Examples Foreword Preface to Volume I xiii xvi xvii xix xxiii
More informationMulti-Regime Analysis
Multi-Regime Analysis Applications to Fixed Income 12/7/2011 Copyright 2011, Hipes Research 1 Credit This research has been done in collaboration with my friend, Thierry F. Bollier, who was the first to
More informationA Markov Chain Monte Carlo Approach to Estimate the Risks of Extremely Large Insurance Claims
International Journal of Business and Economics, 007, Vol. 6, No. 3, 5-36 A Markov Chain Monte Carlo Approach to Estimate the Risks of Extremely Large Insurance Claims Wan-Kai Pang * Department of Applied
More informationStochastic Volatility Models. Hedibert Freitas Lopes
Stochastic Volatility Models Hedibert Freitas Lopes SV-AR(1) model Nonlinear dynamic model Normal approximation R package stochvol Other SV models STAR-SVAR(1) model MSSV-SVAR(1) model Volume-volatility
More informationMarket Risk Analysis Volume IV. Value-at-Risk Models
Market Risk Analysis Volume IV Value-at-Risk Models Carol Alexander John Wiley & Sons, Ltd List of Figures List of Tables List of Examples Foreword Preface to Volume IV xiii xvi xxi xxv xxix IV.l Value
More informationEstimating a Dynamic Oligopolistic Game with Serially Correlated Unobserved Production Costs. SS223B-Empirical IO
Estimating a Dynamic Oligopolistic Game with Serially Correlated Unobserved Production Costs SS223B-Empirical IO Motivation There have been substantial recent developments in the empirical literature on
More informationWeb Appendix to Components of bull and bear markets: bull corrections and bear rallies
Web Appendix to Components of bull and bear markets: bull corrections and bear rallies John M. Maheu Thomas H. McCurdy Yong Song 1 Bull and Bear Dating Algorithms Ex post sorting methods for classification
More information