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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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    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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