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2015 | 7 | nr 1 | 43--70
Tytuł artykułu

Bayesian DEJD Model and Detection of Asymmetry in Jump Sizes

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
News might trigger jump arrivals in financial time series. The "bad" news and "good" news seem to have distinct impact. In the research, a double exponential jump distribution is applied to model downward and upward jumps. Bayesian double exponential jump-diffusion model is proposed. Theorems stated in the paper enable estimation of the model's parameters, detection of jumps and analysis of jump frequency. The methodology, founded upon the idea of latent variables, is illustrated with simulated data. (original abstract)
Rocznik
Tom
7
Numer
Strony
43--70
Opis fizyczny
Twórcy
  • Cracow University of Economics, Poland
Bibliografia
  • [1] Ait-Sahalia Y. and Jacod J. (2012): Analyzing the Spectrum of Asset Returns: Jump and Volatility Components in High Frequency Data, Journal of Economic Literature, 50, 1007-1050.
  • [2] Ane T. and Metais C. (2010): Jump Distribution Characteristics: Evidence from European Stock Markets, International Journal of Business and Economics, 9(1), 1-22.
  • [3] Ball C. and Torous W. (1983): A simplified Jump Process for Common Stock Returns, Journal of Financial and Quantitative Analysis, 1(18), 53-65.
  • [4] Barndorff-Nielsen O. and Shephard N. (2004): Power and Bipower Variation with Stochastic Volatility and Jumps, Journal of Financial Econometrics, 2, 1-37.
  • [5] Barndorff-Nielsen O. and Shephard N. (2006a): Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation, Journal of Financial Econometrics, 4, 1-30.
  • [6] Barndorff-Nielsen O. and Shephard N. (2006b): Impact of Jumps on Returns and Realised Variances: Econometric Analysis of Time-Deformed Levy Processes, Journal of Econometrics, 131, 217-252.
  • [7] Bernardo J. and Smith A. (2002): Bayesian Theory. Wiley Series in Probability and Statistics.
  • [8] Będowska-Sójka B. (2012): Jumps in Stock Returns: Evidence from the Polish Stock Exchangepp. 121-135, no. 10 [in:] FindEcon Monograph Series: Advances in Financial Market Analysis. Lodz University Press.
  • [9] Black F. and Scholes M. (1973): The Pricing of Options and Corporate Liabilities, Journal of Political Economy, 81(3), 637-654.
  • [10] Chib S. and Greenberg E. (1995): Understanding the Metropolis-Hastings Algorithm, The American Statistician, 49, 327-335.
  • [11] Frame S. and Ramezani C. (2012): Bayesian Estimation of Asymmetric Jump-Diffusion Processes, Working paper. http://cyrus.cob.calpoly.edu/MCMC/Frame-Ramezani-Bayesian Estimation of Asymmetric Jump-Diffusion Processes .pdf.
  • [12] Frühwirth-Schnatter S. (2006): Finite Mixtures and Markov Switching Models, Springer Series in Statistics. New York/Berlin/Heidelberg.
  • [13] Gamerman D. and Lopes H. (2006): Markov Chain Monte Carlo. Stochastic Simulation for Bayesian Inference. Chapman & Hall/CRC.
  • [14] Hanson F. and Westman J. (2002): Stochastic Analysis of Jump- Diffusions for Financial Log-Return Processes, [in:] Stochastic Theory and Control: Proceedings of a Workshop held in Lawrence, Kansas, [ed.] Pasik-Duncan B., vol. 280 of Lecture Notes in Control and Information Sciences, pp. 169-184. Springer-Verlag, New York.
  • [15] Hanson F., Westman J. and Zhu Z. (2004): Multinomial maximum likelihood estimation of market parameters for stock jump-diffusion models, [in:] Mathematics of Finance. Proceedings of the 2003 AMS-IMS-SIAM Joint Summer Research Seminar in Applied Mathematics, [ed.] Yin G. and Zhang Q., vol. 351 of Contemporary Mathematics, pp. 155-169. American Mathematical Society, Providence, RI.
  • [16] Honore P. (1998): Pitfalls in Estimating Jump-Diffusion Models, Working Paper Series no 18. The Aarhus School of Business. http://www.stat.purdue.edu/figueroa/Teaching/Stat598F/HonoreJmpDffsEst.pdf
  • [17] Jackwerth J. and Rubinstein M. (1996): Recovering Probability Distributions from Contemporary Security Prices, Journal of Finance, 51, 347-369.
  • [18] Johannes M. and Polson N. (2010): MCMC Methods for Continuous- Time Financial Econometrics, [in:] Handbook of Financial Econometrics, [ed.] Ait-Sahalia Y. and Hansen L., vol. 2, pp. 1-72. North Holland.
  • [19] Kostrzewski M. (2012a): Bayesian Pricing of the Optimal-Replication Strategy for European Option in the JD(M)J Model, Dynamic Econometric Models, 12, 53-71.
  • [20] Kostrzewski M. (2012b): On the Existence of Jumps in Financial Time Series, Acta Physica Polonica B, 43, 2001-2019, DOI: 10.5506/APhysPolB.43.2001.
  • [21] Kostrzewski M. (2014a): Bayesian Inference for the Jump-Diffusion Model with M Jumps, Communications in Statistics - Theory and Methods, 43, 3955-3985, DOI: 10.1080/03610926.2012.755202
  • [22] Kostrzewski M. (2014b): The Hawkes Process and Time-Varying Jump Intensity in Financial Time Series, [in:] 8-th International Days of Statistics and Economics, [ed.] Loster T. and Pavelka T., pp. 743-754, Prague, Czech Republic. Melandrium, http://msed.vse.cz/msed2014/article/324-Kostrzewski-Maciej-paper.pdf
  • [23] Kostrzewski M. (2014c): Some Method of Detecting the Jump Clustering Phenomenon in Financial Time Series, [in:] 17-th International Scientific Conference Applications of Mathematics and Statistics in Economics, [ed.] Rusnak Z. and Zmyślona B., pp. 141-150, Wrocław, Poland. Wrocław University of Economics, DOI: 10.15611/amse.2014.17.15.
  • [24] Kou S. (2002): A jump-diffusion model for option pricing. Management Science, 48, 1086-1101.
  • [25] Lee S. (2012): Jumps and Information Flow in Financial Markets, Review of Financial Studies, 25, 311-344.
  • [26] Lin S. and Huang M. (2002): Estimating Jump-Diffusion Models Using the MCMC Simulation, Working paper 0215E. National Tsing Hua University Department of Economics NTHU Working Paper Series.
  • [27] Merton R. (1976): Option pricing when underlying stock return rates are discontinuous, Journal of Financial Economics, 3, 125-144.
  • [28] Milgrom P. (1981): Good news and bad news: Representation theorems and applications, Bell Journal of Economics, 12, 380-391.
  • [29] Piazzesi M. (2005): Bond Yields and the Federal Reserve, Journal of Political Economy, 113, 311-344.
  • [30] Ramezani C. and Zeng Y. (2007): Maximum likelihood estimation of the double exponential jump-diffusion process, Annals of Finance, 3, 487-507.
  • [31] Ramezani C. and Zeng Y. (1998): Maximum Likelihood Estimation of Asymmetric Jump-Diffusion Models, Working paper http://cyrus.cob.calpoly.edu/JUMPMLE/Ramezani-Zeng-PBJD.pdf
  • [32] Rifo L. and Torres S. (2009): Full Bayesian Analysis for a Class of Jump-Diffusion Models, Communications in Statistics - Theory and Methods, 38, 1262-1271.
  • [33] Synowiec D. (2008): Jump-diffusion models with constant parameters for financial log-return processes, Computers and Mathematics with Applications, 56, 2120-2127.
  • [34] Weron R. (2008): Market price of risk implied by Asian-style electricity options and futures, Energy Economics, 30, 1098-1115.
  • [36] Yu B. and Mykland P. (1998): Looking at Markov Samplers Through Cumsum Path Plots: A Simple Diagnostic Idea, Statistics and Computing, 8, 275-286.
  • [36] Yu J. (2007): Closed-form likelihood approximation and estimation of jump-diffusions with an application to the realignment risk of the Chinese yuan, Journal of Econometrics, 141, 1245-1280.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.ekon-element-000171356101

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