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Can volatility spread fully capture the put–call parity violation?

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  • Liu, Shican
  • Zhu, Songping

Abstract

Put–call parity (PCP) is a well-known relationship between call and put option prices and their underlying for complete markets. It is equally well known for its violation in incomplete markets. However, unlike all the previously documented reasons in the literature, we show in this paper, through convincing empirical evidence, that the density spread of the put and call is also “blamed” for such a violation. We also provide a theoretical framework to financially explain such an imbalance in incomplete markets.

Suggested Citation

  • Liu, Shican & Zhu, Songping, 2025. "Can volatility spread fully capture the put–call parity violation?," The North American Journal of Economics and Finance, Elsevier, vol. 80(C).
    • Handle: RePEc:eee:ecofin:v:80:y:2025:i:c:s1062940825001330
    DOI: 10.1016/j.najef.2025.102493
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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Dario Caldara & Matteo Iacoviello, 2022. "Measuring Geopolitical Risk," American Economic Review, American Economic Association, vol. 112(4), pages 1194-1225, April.
    3. George P Gao & Pengjie Gao & Zhaogang Song, 2018. "Do Hedge Funds Exploit Rare Disaster Concerns?," The Review of Financial Studies, Society for Financial Studies, vol. 31(7), pages 2650-2692.
    4. Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, vol. 1(4), pages 423-432, October.
    5. Barletta, Andrea & Santucci de Magistris, Paolo & Violante, Francesco, 2019. "A non-structural investigation of VIX risk neutral density," Journal of Banking & Finance, Elsevier, vol. 99(C), pages 1-20.
    6. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    7. Chaohua Dong & Jiti Gao, 2025. "Additive Nonparametric Models," Advanced Studies in Theoretical and Applied Econometrics, in: Modern Series Methods in Econometrics and Statistics, chapter 0, pages 141-173, Springer.
    8. Steven L. Heston & Alberto G. Rossi, 2017. "A Spanning Series Approach to Options," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 7(1), pages 2-42.
    9. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    10. Aït-Sahalia, Yacine & Matthys, Felix & Osambela, Emilio & Sircar, Ronnie, 2025. "When uncertainty and volatility are disconnected: Implications for asset pricing and portfolio performance," Journal of Econometrics, Elsevier, vol. 248(C).
    11. Lu, Junwen & Qu, Zhongjun, 2021. "Sieve estimation of option-implied state price density," Journal of Econometrics, Elsevier, vol. 224(1), pages 88-112.
    12. Xingzhi Yao & Marwan Izzeldin, 2018. "Forecasting using alternative measures of model‐free option‐implied volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(2), pages 199-218, February.
    13. Jose M. Marin & Jacques P. Olivier, 2008. "The Dog That Did Not Bark: Insider Trading and Crashes," Journal of Finance, American Finance Association, vol. 63(5), pages 2429-2476, October.
    14. Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," The Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
    15. Bevilacqua, Mattia & Tunaru, Radu, 2021. "The SKEW index: Extracting what has been left," Journal of Financial Stability, Elsevier, vol. 53(C).
    16. Cortés, Lina M. & Mora-Valencia, Andrés & Perote, Javier, 2020. "Retrieving the implicit risk neutral density of WTI options with a semi-nonparametric approach," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    17. Wagner, Drew & Ellis, David M & Dubofsky, David A, 1996. "The Factors behind Put-Call Parity Violations of S&P 100 Index Options," The Financial Review, Eastern Finance Association, vol. 31(3), pages 535-552, August.
    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. Tim Bollerslev & Viktor Todorov, 2011. "Tails, Fears, and Risk Premia," Journal of Finance, American Finance Association, vol. 66(6), pages 2165-2211, December.
    20. George P. Gao & Xiaomeng Lu & Zhaogang Song, 2019. "Tail Risk Concerns Everywhere," Management Science, INFORMS, vol. 65(7), pages 3111-3130, July.
    21. Wen‐Liang G. Hsieh & Chin‐Shen Lee & Shu‐Fang Yuan, 2008. "Price discovery in the options markets: An application of put‐call parity," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 28(4), pages 354-375, April.
    22. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    23. Jean-Philippe Aguilar & Justin Lars Kirkby & Jan Korbel, 2020. "Pricing, Risk and Volatility in Subordinated Market Models," Risks, MDPI, vol. 8(4), pages 1-27, November.
    24. Lu, Quanying & Li, Yuze & Chai, Jian & Wang, Shouyang, 2020. "Crude oil price analysis and forecasting: A perspective of “new triangle”," Energy Economics, Elsevier, vol. 87(C).
    25. Kamara, Avraham & Miller, Thomas W., 1995. "Daily and Intradaily Tests of European Put-Call Parity," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(4), pages 519-539, December.
    26. Brunetti, Marianna & Torricelli, Costanza, 2005. "Put-call parity and cross-markets efficiency in the index options markets: evidence from the Italian market," International Review of Financial Analysis, Elsevier, vol. 14(5), pages 508-532.
    27. Steven L. Heston & Alberto G. Rossi, 2017. "A Spanning Series Approach to Options," The Review of Asset Pricing Studies, Oxford University Press, vol. 7(1), pages 2-42.
    28. Alexander, Carol & Nogueira, Leonardo M., 2007. "Model-free hedge ratios and scale-invariant models," Journal of Banking & Finance, Elsevier, vol. 31(6), pages 1839-1861, June.
    29. Bevilacqua, Mattia & Tunaru, Radu, 2021. "The SKEW index: extracting what has been left," LSE Research Online Documents on Economics 108198, London School of Economics and Political Science, LSE Library.
    30. Cremers, Martijn & Weinbaum, David, 2010. "Deviations from Put-Call Parity and Stock Return Predictability," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(2), pages 335-367, April.
    31. Chin‐Ho Chen & Huimin Chung & Shu‐Fang Yuan, 2014. "Deviations from Put–Call Parity and Volatility Prediction: Evidence from the Taiwan Index Option Market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(12), pages 1122-1145, December.
    32. Klemkosky, Robert C & Resnick, Bruce G, 1979. "Put-Call Parity and Market Efficiency," Journal of Finance, American Finance Association, vol. 34(5), pages 1141-1155, December.
    33. Dierkes, Maik & Hollstein, Fabian & Prokopczuk, Marcel & Würsig, Christoph Matthias, 2024. "Measuring tail risk," Journal of Econometrics, Elsevier, vol. 241(2).
    34. Dilip B. Madan & King Wang, 2021. "Option Implied Vix, Skew And Kurtosis Term Structures," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 24(05), pages 1-13, August.
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