IDEAS home Printed from https://ideas.repec.org/a/nea/journl/y2023i60p27-48.html
   My bibliography  Save this article

Composite option pricing and the volatility surface construction

Author

Listed:
  • Kopaliani, R.

    (Bank Saint Petersburg, Saint Petersburg, Russia)

  • Denisov, N.

    (Bank Saint Petersburg, Saint Petersburg, Russia)

Abstract

This paper proposes a methodology for constructing a cross-asset volatility surface. This volatility surface makes it possible to evaluate the price and risk metrics of options for assets, which do not have a liquid options market and can be created through the composition of two liquid assets. A version of the derivation of an analytical formula for estimating the value of a European option on a cross-asset and expressions for calculating risk measures ("Greeks") are proposed. The key parameters for constructing a cross-asset surface are the correlation between the components of the cross-asset and the implied volatilities of the components of the cross-asset. Different approaches are presented for estimating the correlation coefficient: using historical correlation, dynamic conditional correlation model, and implied correlation. It is demonstrated that if the volatility "at the money" of a cross-asset is known, then the implied correlation is calculated explicitly, otherwise historical correlation or the DCC-GARCH (1,1) model can be used. It is shown that by fixing the implied volatility "at the money" of a less risky asset and varying the implied volatility of a riskier asset, the cross-asset volatility surface is obtained that is closest to the observed one. The article presents strict theoretical calculations and makes it possible to evaluate composite options price in practice.

Suggested Citation

  • Kopaliani, R. & Denisov, N., 2023. "Composite option pricing and the volatility surface construction," Journal of the New Economic Association, New Economic Association, vol. 60(3), pages 27-48.
    • Handle: RePEc:nea:journl:y:2023:i:60:p:27-48
    DOI: 10.31737/22212264_2023_3_27-48
    as

    Download full text from publisher

    File URL: http://www.econorus.org/repec/journl/2023-60-27-48r.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.31737/22212264_2023_3_27-48?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
    ---><---

    References listed on IDEAS

    as
    1. Dilip B. Madan & King Wang, 2021. "Pricing Product Options and Using Them to Complete Markets for Functions of Two Underlying Asset Prices," JRFM, MDPI, vol. 14(8), pages 1-20, August.
    2. Nagapetyan, Artur, 2019. "Precondition stock and stock indices volatility modeling based on market diversification potential: Evidence from Russian market," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 56, pages 45-61.
    3. 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.
    4. Sergio Pulido, 2010. "The fundamental theorem of asset pricing, the hedging problem and maximal claims in financial markets with short sales prohibitions," Papers 1012.3102, arXiv.org, revised Jan 2014.
    5. Stephen J. Taylor & Yaw‐Huei Wang, 2010. "Option prices and risk‐neutral densities for currency cross rates," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(4), pages 324-360, April.
    6. U. Cherubini & E. Luciano, 2002. "Bivariate option pricing with copulas," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(2), pages 69-85.
    7. Castrén, Olli & Mazzotta, Stefano, 2005. "Foreign exchange option and returns based correlation forecasts: evaluation and two applications," Working Paper Series 447, European Central Bank.
    8. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    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. Turan G. Bali & Hao Zhou, 2011. "Risk, uncertainty, and expected returns," Finance and Economics Discussion Series 2011-45, Board of Governors of the Federal Reserve System (U.S.).
    2. Gagnon, Marie-Hélène & Power, Gabriel J. & Toupin, Dominique, 2023. "The sum of all fears: Forecasting international returns using option-implied risk measures," Journal of Banking & Finance, Elsevier, vol. 146(C).
    3. Jianlei Han & Martina Linnenluecke & Zhangxin Liu & Zheyao Pan & Tom Smith, 2019. "A general equilibrium approach to pricing volatility risk," PLOS ONE, Public Library of Science, vol. 14(4), pages 1-18, April.
    4. Avdulaj, Krenar & Barunik, Jozef, 2015. "Are benefits from oil–stocks diversification gone? New evidence from a dynamic copula and high frequency data," Energy Economics, Elsevier, vol. 51(C), pages 31-44.
    5. Tavin, Bertrand, 2015. "Detection of arbitrage in a market with multi-asset derivatives and known risk-neutral marginals," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 158-178.
    6. Wolfgang Karl Hardle & Elena Silyakova, 2020. "Implied Basket Correlation Dynamics," Papers 2009.09770, arXiv.org.
    7. Härdle Wolfgang Karl & Silyakova Elena, 2016. "Implied basket correlation dynamics," Statistics & Risk Modeling, De Gruyter, vol. 33(1-2), pages 1-20, September.
    8. repec:hum:wpaper:sfb649dp2012-066 is not listed on IDEAS
    9. Shiraya, Kenichiro & Yamakami, Tomohisa, 2024. "Constructing copulas using corrected Hermite polynomial expansion for estimating cross foreign exchange volatility," European Journal of Operational Research, Elsevier, vol. 314(3), pages 1195-1214.
    10. Leonidas Tsiaras, 2010. "Dynamic Models of Exchange Rate Dependence Using Option Prices and Historical Returns," CREATES Research Papers 2010-35, Department of Economics and Business Economics, Aarhus University.
    11. Chung, San-Lin & Wang, Yaw-Huei, 2008. "Bounds and prices of currency cross-rate options," Journal of Banking & Finance, Elsevier, vol. 32(5), pages 631-642, May.
    12. Härdle, Wolfgang Karl & Silyakova, Elena, 2012. "Implied basket correlation dynamics," SFB 649 Discussion Papers 2012-066, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    13. Rob van den Goorbergh, 2004. "A Copula-Based Autoregressive Conditional Dependence Model of International Stock Markets," DNB Working Papers 022, Netherlands Central Bank, Research Department.
    14. Sara Cecchetti & Laura Sigalotti, 2013. "Forward-looking robust portfolio selection," Temi di discussione (Economic working papers) 913, Bank of Italy, Economic Research and International Relations Area.
    15. Bisht Deepak & Laha, A. K., 2017. "Assessment of Density Forecast for Energy Commodities in Post-Financialization Era," IIMA Working Papers WP 2017-07-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    16. Allan M. Malz, 2013. "Risk-neutral systemic risk indicators," Staff Reports 607, Federal Reserve Bank of New York.
    17. Alexander M. G. Cox & Zhaoxu Hou & Jan Obloj, 2014. "Robust pricing and hedging under trading restrictions and the emergence of local martingale models," Papers 1406.0551, arXiv.org, revised Jun 2015.
    18. Kenichiro Shiraya & Tomohisa Yamakami, 2023. "Constructing Copulas Using Corrected Hermite Polynomial Expansion for Estimating Cross Foreign Exchange Volatility," Papers 2301.10044, arXiv.org.
    19. Han, Chulwoo & Park, Frank C., 2022. "A geometric framework for covariance dynamics," Journal of Banking & Finance, Elsevier, vol. 134(C).
    20. Chunhachinda, Pornchai & de Boyrie, Maria E. & Pavlova, Ivelina, 2019. "Measuring the hedging effectiveness of commodities," Finance Research Letters, Elsevier, vol. 30(C), pages 201-207.
    21. Antonio Rubia & Trino-Manuel Ñíguez, 2006. "Forecasting the conditional covariance matrix of a portfolio under long-run temporal dependence," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(6), pages 439-458.

    More about this item

    Keywords

    cross-asset; exotic option; GARCH; implied volatility; option pricing; implied correlation;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    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:nea:journl:y:2023:i:60:p:27-48. 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: Alexey Tcharykov (email available below). General contact details of provider: https://edirc.repec.org/data/nearuea.html .

    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.