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A tale of two regimes: Theory and empirical evidence for a Markov-modulated jump diffusion model of equity returns and derivative pricing implications

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  • Chang, Charles
  • Fuh, Cheng-Der
  • Lin, Shih-Kuei

Abstract

We provide closed-form solutions for a continuous time, Markov-modulated jump diffusion model in a general equilibrium framework for options prices under a variety of jump diffusion specifications. We further demonstrate that the two-state model provides the leptokurtic return features, volatility smile, and volatility clustering observed empirically for the Dow Jones Industrial Average (DJIA) and its component stocks. Using 10years of stock return data, we confirm the existence of jump intensity switching and clustering, illustrate transition probabilities, and verify superior empirical fit over competing Poisson-style models.

Suggested Citation

  • Chang, Charles & Fuh, Cheng-Der & Lin, Shih-Kuei, 2013. "A tale of two regimes: Theory and empirical evidence for a Markov-modulated jump diffusion model of equity returns and derivative pricing implications," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3204-3217.
    • Handle: RePEc:eee:jbfina:v:37:y:2013:i:8:p:3204-3217
    DOI: 10.1016/j.jbankfin.2013.03.009
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    1. Philip H. Dybvig, Chi-fu Huang, 1988. "Nonnegative Wealth, Absence of Arbitrage, and Feasible Consumption Plans," The Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 377-401.
    2. Chan, Wing H., 2004. "Conditional correlated jump dynamics in foreign exchange," Economics Letters, Elsevier, vol. 83(1), pages 23-28, April.
    3. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
    4. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    5. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    6. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    7. Hui Chen, 2010. "Macroeconomic Conditions and the Puzzles of Credit Spreads and Capital Structure," Journal of Finance, American Finance Association, vol. 65(6), pages 2171-2212, December.
    8. repec:bla:jfinan:v:59:y:2004:i:3:p:1367-1404 is not listed on IDEAS
    9. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    10. Beckers, Stan, 1981. "A Note on Estimating the Parameters of the Diffusion-Jump Model of Stock Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 16(1), pages 127-140, March.
    11. Wing H. Chan, 2003. "A correlated bivariate Poisson jump model for foreign exchange," Empirical Economics, Springer, vol. 28(4), pages 669-685, November.
    12. Naik, Vasanttilak & Lee, Moon, 1990. "General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 493-521.
    13. Ball, Clifford A & Torous, Walter N, 1985. "On Jumps in Common Stock Prices and Their Impact on Call Option Pricing," Journal of Finance, American Finance Association, vol. 40(1), pages 155-173, March.
    14. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    15. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239, April.
    16. Bates, David S, 1991. "The Crash of '87: Was It Expected? The Evidence from Options Markets," Journal of Finance, American Finance Association, vol. 46(3), pages 1009-1044, July.
    17. Robert Elliott & Tak Siu, 2011. "A risk-based approach for pricing American options under a generalized Markov regime-switching model," Quantitative Finance, Taylor & Francis Journals, vol. 11(11), pages 1633-1646.
    18. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    19. Ball, Clifford A. & Torous, Walter N., 1983. "A Simplified Jump Process for Common Stock Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(1), pages 53-65, March.
    20. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," The Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
    21. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    22. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    23. Xiaowei Ding & Kay Giesecke & Pascal I. Tomecek, 2009. "Time-Changed Birth Processes and Multiname Credit Derivatives," Operations Research, INFORMS, vol. 57(4), pages 990-1005, August.
    24. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
    25. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    26. Bo, Lijun & Wang, Yongjin & Yang, Xuewei, 2010. "Markov-modulated jump-diffusions for currency option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 461-469, June.
    27. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 383-410, July.
    28. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
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    Cited by:

    1. Hsu, Yuan-Lin & Lin, Shih-Kuei & Hung, Ming-Chin & Huang, Tzu-Hui, 2016. "Empirical analysis of stock indices under a regime-switching model with dependent jump size risks," Economic Modelling, Elsevier, vol. 54(C), pages 260-275.
    2. Ben-zhang Yang & Jia Yue & Ming-hui Wang & Nan-jing Huang, 2018. "Volatility swaps valuation under stochastic volatility with jumps and stochastic intensity," Papers 1805.06226, arXiv.org, revised May 2018.
    3. Lian, Yu-Min & Liao, Szu-Lang & Chen, Jun-Home, 2015. "State-dependent jump risks for American gold futures option pricing," The North American Journal of Economics and Finance, Elsevier, vol. 33(C), pages 115-133.
    4. Siu, Tak Kuen, 2023. "European option pricing with market frictions, regime switches and model uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 233-250.
    5. Son-Nan Chen & Pao-Peng Hsu & Chang-Yi Li, 2016. "Pricing credit-risky bonds and spread options modelling credit-spread term structures with two-dimensional Markov-modulated jump-diffusion," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 573-592, April.
    6. Yang, Ben-Zhang & Yue, Jia & Wang, Ming-Hui & Huang, Nan-Jing, 2019. "Volatility swaps valuation under stochastic volatility with jumps and stochastic intensity," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 73-84.
    7. Chen, Jun-Home & Lian, Yu-Min & Liao, Szu-Lang, 2022. "Pricing catastrophe equity puts with counterparty risks under Markov-modulated, default-intensity processes," The North American Journal of Economics and Finance, Elsevier, vol. 61(C).
    8. Shih-Kuei Lin & Yu-Min Lian & Szu-Lang Liao, 2014. "Pricing gold options under Markov-modulated jump-diffusion processes," Applied Financial Economics, Taylor & Francis Journals, vol. 24(12), pages 825-836, June.
    9. Huang, Chun-Sung & O'Hara, John G. & Mataramvura, Sure, 2022. "Highly efficient Shannon wavelet-based pricing of power options under the double exponential jump framework with stochastic jump intensity and volatility," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    10. Ayub Ahmadi & Mahdieh Tahmasebi, 2024. "Pricing and delta computation in jump-diffusion models with stochastic intensity by Malliavin calculus," Papers 2405.00473, arXiv.org.
    11. Lin, Shih-Kuei & Peng, Jin-Lung & Chao, Wei-Hsiung & Wu, An-Chi, 2016. "The extension from independence to dependence between jump frequency and jump size in Markov-modulated jump diffusion models," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 217-235.

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    More about this item

    Keywords

    Markov-modulated; Jump diffusion; Volatility clustering; Jump clustering; Volatility smile; Options pricing;
    All these keywords.

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models
    • G01 - Financial Economics - - General - - - Financial Crises
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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