IDEAS home Printed from https://ideas.repec.org/a/eee/ecmode/v51y2015icp263-268.html
   My bibliography  Save this article

On the stochastic elasticity of variance diffusions

Author

Listed:
  • Kim, Jeong-Hoon
  • Yoon, Ji-Hun
  • Lee, Jungwoo
  • Choi, Sun-Yong

Abstract

The elasticity of variance of risky assets has been observed to be rapidly fluctuating around a level. The level itself slowly varies depending upon the corresponding economic situation at the time of consideration. In particular, it turns out to be extraordinary during the peak period of the 2007–2009 Global Financial Crisis. Based on the concept of stochastic elasticity of variance, this paper develops an asset price model in a multiscale form and applies it to the pricing of European options and verifies a significant improvement over the constant elasticity of variance model in terms of the geometric structure (skew or smirk) of implied volatility. Our result implies that a theoretical model based on the random elasticity can derive market's volatility forecast more accurately than the constant elasticity so that investors can employ a dynamic investment strategy reducing risk more effectively.

Suggested Citation

  • Kim, Jeong-Hoon & Yoon, Ji-Hun & Lee, Jungwoo & Choi, Sun-Yong, 2015. "On the stochastic elasticity of variance diffusions," Economic Modelling, Elsevier, vol. 51(C), pages 263-268.
    • Handle: RePEc:eee:ecmode:v:51:y:2015:i:c:p:263-268
    DOI: 10.1016/j.econmod.2015.08.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0264999315002230
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econmod.2015.08.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584, January.
    2. Harvey, Campbell R., 2001. "The specification of conditional expectations," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 573-637, December.
    3. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    4. Emanuel, David C. & MacBeth, James D., 1982. "Further Results on the Constant Elasticity of Variance Call Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(4), pages 533-554, November.
    5. repec:bla:jfinan:v:44:y:1989:i:5:p:1177-89 is not listed on IDEAS
    6. Campbell, John Y., 1987. "Stock returns and the term structure," Journal of Financial Economics, Elsevier, vol. 18(2), pages 373-399, June.
    7. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    8. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    9. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous‐time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323, October.
    10. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    11. repec:bla:jfinan:v:44:y:1989:i:1:p:211-19 is not listed on IDEAS
    12. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    13. Brandt, Michael W. & Kang, Qiang, 2004. "On the relationship between the conditional mean and volatility of stock returns: A latent VAR approach," Journal of Financial Economics, Elsevier, vol. 72(2), pages 217-257, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Marcos Escobar-Anel & Weili Fan, 2023. "The SEV-SV Model—Applications in Portfolio Optimization," Risks, MDPI, vol. 11(2), pages 1-34, January.
    2. Min-Ku Lee, 2019. "Pricing Perpetual American Lookback Options Under Stochastic Volatility," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 1265-1277, March.
    3. Kim, Donghyun & Choi, Sun-Yong & Yoon, Ji-Hun, 2021. "Pricing of vulnerable options under hybrid stochastic and local volatility," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    4. Cao, Jiling & Kim, Jeong-Hoon & Kim, See-Woo & Zhang, Wenjun, 2020. "Rough stochastic elasticity of variance and option pricing," Finance Research Letters, Elsevier, vol. 37(C).
    5. Seo, Jun-Ho & Kim, Jeong-Hoon, 2022. "Multiscale stochastic elasticity of variance for options and equity linked annuity; A Mellin transform approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 303-320.
    6. Kim, Seong-Tae & Kim, Jeong-Hoon, 2020. "Stochastic elasticity of vol-of-vol and pricing of variance swaps," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 420-440.
    7. Xia, Kun & Yang, Xuewei & Zhu, Peng, 2023. "Delta hedging and volatility-price elasticity: A two-step approach," Journal of Banking & Finance, Elsevier, vol. 153(C).
    8. Min-Ku LEE & Sung-Jin YANG, PhD & Jeong-Hoon KIM, 2017. "Pricing Vulnerable Options with Constant Elasticity of Variance versus Stochastic Elasticity of Variance," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 51(1), pages 233-247.
    9. Sun-Yong Choi & Sotheara Veng & Jeong-Hoon Kim & Ji-Hun Yoon, 2022. "A Mellin Transform Approach to the Pricing of Options with Default Risk," Computational Economics, Springer;Society for Computational Economics, vol. 59(3), pages 1113-1134, March.
    10. Yoon, Ji-Hun & Park, Chang-Rae, 2016. "Pricing turbo warrants under stochastic elasticity of variance," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 107-118.
    11. Cao, Jiling & Kim, Jeong-Hoon & Li, Xi & Zhang, Wenjun, 2023. "Valuation of barrier and lookback options under hybrid CEV and stochastic volatility," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 660-676.
    12. Kim, Donghyun & Shin, Yong Hyun & Yoon, Ji-Hun, 2024. "The valuation of real options for risky barrier to entry with hybrid stochastic and local volatility and stochastic investment costs," The North American Journal of Economics and Finance, Elsevier, vol. 70(C).
    13. Kim, Donghyun & Ha, Mijin & Kim, Jeong-Hoon & Yoon, Ji-Hun, 2024. "A local volatility correction to mean-reverting stochastic volatility model for pricing derivatives," The Quarterly Review of Economics and Finance, Elsevier, vol. 97(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jeong‐Hoon Kim & Jungwoo Lee & Song‐Ping Zhu & Seok‐Hyon Yu, 2014. "A multiscale correction to the Black–Scholes formula," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 30(6), pages 753-765, November.
    2. Kim, Donghyun & Shin, Yong Hyun & Yoon, Ji-Hun, 2024. "The valuation of real options for risky barrier to entry with hybrid stochastic and local volatility and stochastic investment costs," The North American Journal of Economics and Finance, Elsevier, vol. 70(C).
    3. Kim, Donghyun & Ha, Mijin & Kim, Jeong-Hoon & Yoon, Ji-Hun, 2024. "A local volatility correction to mean-reverting stochastic volatility model for pricing derivatives," The Quarterly Review of Economics and Finance, Elsevier, vol. 97(C).
    4. Peter F. Christoffersen & Francis X. Diebold, 2006. "Financial Asset Returns, Direction-of-Change Forecasting, and Volatility Dynamics," Management Science, INFORMS, vol. 52(8), pages 1273-1287, August.
    5. Amit K. Sinha, 2021. "The reliability of geometric Brownian motion forecasts of S&P500 index values," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(8), pages 1444-1462, December.
    6. Brenner, Menachem & Izhakian, Yehuda, 2018. "Asset pricing and ambiguity: Empirical evidence⁎," Journal of Financial Economics, Elsevier, vol. 130(3), pages 503-531.
    7. Bali, Turan G. & Engle, Robert F., 2010. "The intertemporal capital asset pricing model with dynamic conditional correlations," Journal of Monetary Economics, Elsevier, vol. 57(4), pages 377-390, May.
    8. Su, EnDer & Wen Wong, Kai, 2019. "Testing the alternative two-state options pricing models: An empirical analysis on TXO," The Quarterly Review of Economics and Finance, Elsevier, vol. 72(C), pages 101-116.
    9. Ang, Andrew & Liu, Jun, 2007. "Risk, return, and dividends," Journal of Financial Economics, Elsevier, vol. 85(1), pages 1-38, July.
    10. Yueh-Neng Lin & Ken Hung, 2008. "Is Volatility Priced?," Annals of Economics and Finance, Society for AEF, vol. 9(1), pages 39-75, May.
    11. Tobias Adrian & Joshua Rosenberg, 2008. "Stock Returns and Volatility: Pricing the Short‐Run and Long‐Run Components of Market Risk," Journal of Finance, American Finance Association, vol. 63(6), pages 2997-3030, December.
    12. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    13. Kim, Jeong-Hoon & Lee, Min-Ku & Sohn, So Young, 2014. "Investment timing under hybrid stochastic and local volatility," Chaos, Solitons & Fractals, Elsevier, vol. 67(C), pages 58-72.
    14. repec:ehu:dfaeii:6728 is not listed on IDEAS
    15. Rui Vilela Mendes & M. J. Oliveira, 2006. "A data-reconstructed fractional volatility model," Papers math/0602013, arXiv.org, revised Jun 2007.
    16. Thomas C. Chiang & Jiandong Li, 2012. "Stock Returns and Risk: Evidence from Quantile," JRFM, MDPI, vol. 5(1), pages 1-39, December.
    17. Wang, Wenzhao & Duxbury, Darren, 2021. "Institutional investor sentiment and the mean-variance relationship: Global evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 415-441.
    18. Yu, Jianfeng & Yuan, Yu, 2011. "Investor sentiment and the mean-variance relation," Journal of Financial Economics, Elsevier, vol. 100(2), pages 367-381, May.
    19. Peter Christoffersen & Redouane Elkamhi & Bruno Feunou & Kris Jacobs, 2010. "Option Valuation with Conditional Heteroskedasticity and Nonnormality," The Review of Financial Studies, Society for Financial Studies, vol. 23(5), pages 2139-2183.
    20. Juan Carlos Escanciano & Juan Carlos Pardo-Fernández & Ingrid Van Keilegom, 2017. "Semiparametric Estimation of Risk–Return Relationships," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 40-52, January.
    21. Giulia Di Nunno & Kk{e}stutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From constant to rough: A survey of continuous volatility modeling," Papers 2309.01033, arXiv.org, revised Sep 2023.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecmode:v:51:y:2015:i:c:p:263-268. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/30411 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.