IDEAS home Printed from https://ideas.repec.org/a/eee/ecofin/v48y2019icp819-834.html
   My bibliography  Save this article

Arbitrage-free conditions for implied volatility surface by Delta

Author

Listed:
  • Wang, Ximei
  • Zhao, Yanlong
  • Bao, Ying

Abstract

Implied volatility surface provided by Deltas and maturities (IVS-DM) is widely used in financial fields, especially in foreign exchange options market, since it can effectively describe the characteristics of the volatilities. The main purpose of this paper is to develop arbitrage-free conditions for the IVS-DM. We propose sufficient conditions for the IVS-DM to be static arbitrage-free, which are proved to be necessary under a mild assumption. To test the arbitrage opportunities in the market data, we build a practical tool, which is more accurate than existing ones such as early warning indicator tests. For illustration, arbitrage tests are conducted on a simulated IVS-DM to show the effectiveness of the conditions. The results are consistent with the tests for the implied volatility surface provided by strikes and maturities. Furthermore, empirical examinations are implemented on EURUSD and USDJPY currency options to ensure the feasibility of the proposed conditions.

Suggested Citation

  • Wang, Ximei & Zhao, Yanlong & Bao, Ying, 2019. "Arbitrage-free conditions for implied volatility surface by Delta," The North American Journal of Economics and Finance, Elsevier, vol. 48(C), pages 819-834.
    • Handle: RePEc:eee:ecofin:v:48:y:2019:i:c:p:819-834
    DOI: 10.1016/j.najef.2018.08.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1062940818301074
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.najef.2018.08.011?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. Jacinto Marabel Romo, 2014. "Dynamics of the implied volatility surface. Theory and empirical evidence," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1829-1837, October.
    2. R'uben Sousa & Ana Bela Cruzeiro & Manuel Guerra, 2016. "Barrier Option Pricing under the 2-Hypergeometric Stochastic Volatility Model," Papers 1610.03230, arXiv.org, revised Aug 2017.
    3. Wang, Alan T., 2007. "Does implied volatility of currency futures option imply volatility of exchange rates?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 773-782.
    4. Toby Daglish & John Hull & Wulin Suo, 2007. "Volatility surfaces: theory, rules of thumb, and empirical evidence," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 507-524.
    5. Judith Glaser & Pascal Heider, 2012. "Arbitrage-free approximation of call price surfaces and input data risk," Quantitative Finance, Taylor & Francis Journals, vol. 12(1), pages 61-73, August.
    6. Bianconi, Marcelo & MacLachlan, Scott & Sammon, Marco, 2015. "Implied volatility and the risk-free rate of return in options markets," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 1-26.
    7. Jim Gatheral & Antoine Jacquier, 2014. "Arbitrage-free SVI volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 59-71, January.
    8. Alexander Cox & David Hobson, 2005. "Local martingales, bubbles and option prices," Finance and Stochastics, Springer, vol. 9(4), pages 477-492, October.
    9. Kim, Minho & Kim, Minchoul, 2003. "Implied volatility dynamics in the foreign exchange markets," Journal of International Money and Finance, Elsevier, vol. 22(4), pages 511-528, August.
    10. Hentschel, Ludger, 2003. "Errors in Implied Volatility Estimation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(4), pages 779-810, December.
    11. 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.
    12. Garman, Mark B. & Kohlhagen, Steven W., 1983. "Foreign currency option values," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 231-237, December.
    13. Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1998. "Implied Volatility Functions: Empirical Tests," Journal of Finance, American Finance Association, vol. 53(6), pages 2059-2106, December.
    14. Kotzé, Antonie & Labuschagne, Coenraad C.A. & Nair, Merell L. & Padayachi, Nadine, 2013. "Arbitrage-free implied volatility surfaces for options on single stock futures," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 380-399.
    15. Harry Lo & Aleksandar Mijatović, 2011. "Volatility Derivatives In Market Models With Jumps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(07), pages 1159-1193.
    Full references (including those not matched with items on IDEAS)

    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. Itkin, Andrey, 2015. "To sigmoid-based functional description of the volatility smile," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 264-291.
    2. Chalamandaris, Georgios & Tsekrekos, Andrianos E., 2011. "How important is the term structure in implied volatility surface modeling? Evidence from foreign exchange options," Journal of International Money and Finance, Elsevier, vol. 30(4), pages 623-640, June.
    3. Krylova, Elizaveta & Nikkinen, Jussi & Vähämaa, Sami, 2009. "Cross-dynamics of volatility term structures implied by foreign exchange options," Journal of Economics and Business, Elsevier, vol. 61(5), pages 355-375, September.
    4. Pascal François & Rémi Galarneau‐Vincent & Geneviève Gauthier & Frédéric Godin, 2022. "Venturing into uncharted territory: An extensible implied volatility surface model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(10), pages 1912-1940, October.
    5. Lim, G.C. & Martin, G.M. & Martin, V.L., 2006. "Pricing currency options in the presence of time-varying volatility and non-normalities," Journal of Multinational Financial Management, Elsevier, vol. 16(3), pages 291-314, July.
    6. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
    7. 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.
    8. Chalamandaris, Georgios & Tsekrekos, Andrianos E., 2010. "Predictable dynamics in implied volatility surfaces from OTC currency options," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1175-1188, June.
    9. Mnacho Echenim & Emmanuel Gobet & Anne-Claire Maurice, 2022. "Unbiasing and robustifying implied volatility calibration in a cryptocurrency market with large bid-ask spreads and missing quotes," Papers 2207.02989, arXiv.org.
    10. Elyas Elyasiani & Silvia Muzzioli & Alessio Ruggieri, 2016. "Forecasting and pricing powers of option-implied tree models: Tranquil and volatile market conditions," Department of Economics 0099, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    11. Bernales, Alejandro & Guidolin, Massimo, 2014. "Can we forecast the implied volatility surface dynamics of equity options? Predictability and economic value tests," Journal of Banking & Finance, Elsevier, vol. 46(C), pages 326-342.
    12. Mnacho Echenim & Emmanuel Gobet & Anne-Claire Maurice, 2022. "Unbiasing and robustifying implied volatility calibration in a cryptocurrency market with large bid-ask spreads and missing quotes," Working Papers hal-03715921, HAL.
    13. Jondeau, Eric & Rockinger, Michael, 2000. "Reading the smile: the message conveyed by methods which infer risk neutral densities," Journal of International Money and Finance, Elsevier, vol. 19(6), pages 885-915, December.
    14. Fengler, Matthias R. & Härdle, Wolfgang & Mammen, Enno, 2003. "Implied volatility string dynamics," SFB 373 Discussion Papers 2003,54, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    15. Bender Christian & Thiel Matthias, 2020. "Arbitrage-free interpolation of call option prices," Statistics & Risk Modeling, De Gruyter, vol. 37(1-2), pages 55-78, January.
    16. Shang, Han Lin & Kearney, Fearghal, 2022. "Dynamic functional time-series forecasts of foreign exchange implied volatility surfaces," International Journal of Forecasting, Elsevier, vol. 38(3), pages 1025-1049.
    17. Shane Miller, 2007. "Pricing of Contingent Claims Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2007.
    18. Georgios Chalamandaris & Andrianos Tsekrekos, 2013. "Explanatory Factors and Causality in the Dynamics of Volatility Surfaces Implied from OTC Asian–Pacific Currency Options," Computational Economics, Springer;Society for Computational Economics, vol. 41(3), pages 327-358, March.
    19. Beber, Alessandro & Brandt, Michael W., 2006. "The effect of macroeconomic news on beliefs and preferences: Evidence from the options market," Journal of Monetary Economics, Elsevier, vol. 53(8), pages 1997-2039, November.
    20. Chalamandaris, Georgios & Tsekrekos, Andrianos E., 2009. "Common Factors and Causality in the Dynamics of Implied Volatility Surfaces: Evidence from the FX OTC Market," The Journal of Economic Asymmetries, Elsevier, vol. 6(1), pages 49-74.

    More about this item

    Keywords

    Implied volatility surface; Foreign exchange market; Arbitrage-free condition; Deltas;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

    Statistics

    Access and download statistics

    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:ecofin:v:48:y:2019:i:c:p:819-834. 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/620163 .

    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.