The extension from independence to dependence between jump frequency and jump size in Markov-modulated jump diffusion models |
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| Institution: | 1. Department of Money and Banking, National Chengchi University, Taipei, Taiwan, ROC;2. Department of Risk Management and Insurance, National Chengchi University, Taipei, Taiwan, ROC;3. Department of Applied Mathematics, National Dong Hwa University, Hualien, Taiwan, ROC;1. International Monetary Fund, Washington, United States;2. European University Institute, Florence, Italy;3. De Nederlandsche Bank, Amsterdam, The Netherlands;4. University of Groningen, The Netherlands;5. CESifo, Munich, Germany;1. European Central Bank, Kaiserstrasse 29, D-60311 Frankfurt am Main, Germany;2. Narodowy Bank Polski, Financial Stability Department, ul. Swietokrzyska 11/21, 00-919 Warsaw, Poland;3. Warsaw School of Economics, Institute of Econometrics, ul. Madalińskiego 6/8, 02-513 Warsaw, Poland;1. School of Business and Economics, Department of Accounting and Finance, Thompson Rivers University, 900 McGill Road, Kamloops, BC V2C 5N3, Canada;2. College of Business Administration, Department of Finance, Kent State University, P.O. Box 5190, Kent, OH 44242-0001, USA;3. School of Business and Economics, Department of Economics and Finance, Lynchburg College, 1501 Lakeside Drive, Lynchburg, VA 24551, USA |
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| Abstract: | We set out in this study to investigate the relationship between jump frequency and jump size for the 30 component stocks of the Dow Jones Industrial Average (DJIA) index, extending the Markov-modulated jump diffusion model from independence to dependence between jump frequency and jump size. We propose an estimation method for the parameters of the Markov-modulated jump diffusion model based upon dependence between jump frequency and size, with our results indicating that when abnormal events occur, the Markov-modulated jump diffusion models with both state-independent jump sizes (MJMI) and state-dependent jump sizes (MJMD) outperform the pure jump diffusion (JD) model in terms of capturing the risks of jump frequency and jump size. Based upon Akaike Information Criterion (AIC) and Schwarz Bayesian Criterion (SBC), our results further indicate that for 23 of the component stocks, the MJMD model may be better suited, as compared to the MJMI model. Finally, our empirical observations reveal that the behavior of jump risks in the stock markets, including jump frequency and jump size, is not independent, since these phenomena are found to coincide during both financial crisis periods and stock market crashes, with the largest jump size risks, during certain periods, being accompanied by either systematic or idiosyncratic risks. |
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| Keywords: | Markov-modulated jump models EM-gradient algorithm SEM algorithm |
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