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Are Jumps in Stock Returns Diversifiable? Evidence and Implications for Option Pricing

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  • Kim, Myung-Jig
  • Oh, Young-Ho
  • Brooks, Robert

Abstract

This paper studies the diversifiability of jumps in stock returns. It presents a multivariate time-series model of the stochastic process for an index and its component stocks that explicitly admits discrete common jumps. Maximum likelihood estimation for such a model is developed and applied to the daily Major Market Index and its component stocks for the period 1985 through 1990. The paper finds that Poisson-distributed jumps observed from both the index and its component stocks constitute nondiversifiable risk, implying that the standard assumption in option pricing that these jumps are not priced may be invalid.

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  • Kim, Myung-Jig & Oh, Young-Ho & Brooks, Robert, 1994. "Are Jumps in Stock Returns Diversifiable? Evidence and Implications for Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(4), pages 609-631, December.
    • Handle: RePEc:cup:jfinqa:v:29:y:1994:i:04:p:609-631_00
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    Citations

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    Cited by:

    1. Ramaprasad Bhar, 2010. "Stochastic Filtering with Applications in Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7736, January.
    2. Yin Liao & Heather Anderson & Farshid Vahid, 2010. "Do Jumps Matter? Forecasting Multivariate Realized Volatility Allowing for Common Jumps," ANU Working Papers in Economics and Econometrics 2010-520, Australian National University, College of Business and Economics, School of Economics.
    3. Mandeep S. Chahal & Jun Wang, 1997. "Jump Diffusion Processes and Emerging Bond and Stock Markets: An Investigation Using Daily Data," Multinational Finance Journal, Multinational Finance Journal, vol. 1(3), pages 169-197, September.
    4. Chang, Kook-Hyun & Kim, Myung-Jig, 2001. "Jumps and time-varying correlations in daily foreign exchange rates," Journal of International Money and Finance, Elsevier, vol. 20(5), pages 611-637, October.
    5. Chen, Ke & Vitiello, Luiz & Hyde, Stuart & Poon, Ser-Huang, 2018. "The reality of stock market jumps diversification," Journal of International Money and Finance, Elsevier, vol. 86(C), pages 171-188.
    6. Peter Fortune, 1998. "Weekends can be rough: revisiting the weekend effect in stock prices," Working Papers 98-6, Federal Reserve Bank of Boston.
    7. Consigli, Giorgio, 2002. "Tail estimation and mean-VaR portfolio selection in markets subject to financial instability," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1355-1382, July.
    8. Piccotti, Louis R., 2018. "Jumps, cojumps, and efficiency in the spot foreign exchange market," Journal of Banking & Finance, Elsevier, vol. 87(C), pages 49-67.
    9. Danielsson, Jon & Zigrand, Jean-Pierre, 2006. "On time-scaling of risk and the square-root-of-time rule," Journal of Banking & Finance, Elsevier, vol. 30(10), pages 2701-2713, October.
    10. Eric Jacquier & Cedric Okou, 2013. "Disentangling Continuous Volatility from Jumps in Long-Run Risk-Return Relationships," CIRANO Working Papers 2013s-14, CIRANO.
    11. Tunaru, Radu & Zheng, Teng, 2017. "Parameter estimation risk in asset pricing and risk management: A Bayesian approach," International Review of Financial Analysis, Elsevier, vol. 53(C), pages 80-93.
    12. Marcel Prokopczuk & Yingying Wu, 2013. "Estimating term structure models with the Kalman filter," Chapters, in: Adrian R. Bell & Chris Brooks & Marcel Prokopczuk (ed.), Handbook of Research Methods and Applications in Empirical Finance, chapter 4, pages 97-113, Edward Elgar Publishing.
    13. J.W. Nieuwenhuis & M.H. Vellekoop, 2004. "Weak convergence of tree methods, to price options on defaultable assets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 27(2), pages 87-107, December.
    14. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    15. Peter Fortune, 1999. "Are stock returns different over weekends? a jump diffusion analysis of the \"weekend effect\"," New England Economic Review, Federal Reserve Bank of Boston, issue Sep, pages 3-19.
    16. Chilarescu, Constantin & Viasu, Iana Luciana, 2011. "Phénomènes financiers et mélange de lois : Une nouvelle méthode d’estimation des paramètres," MPRA Paper 33909, University Library of Munich, Germany.
    17. Srivastava, Pranjal & Jacob, Joshy, 2022. "Arbitrage constraints and behaviour of volatility components: Evidence from a natural experiment," IIMA Working Papers WP 2022-10-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    18. Marcel Prokopczuk, 2011. "Optimal portfolio choice in the presence of domestic systemic risk: empirical evidence from stock markets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 34(2), pages 141-168, November.
    19. Sanghoon Lee, 2004. "Approximation of A Jump-Diffusion Process," Econometric Society 2004 Far Eastern Meetings 412, Econometric Society.

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