IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v100y2019icp251-269.html
   My bibliography  Save this article

It only takes a few moments to hedge options

Author

Listed:
  • Barletta, Andrea
  • Santucci de Magistris, Paolo
  • Sloth, David

Abstract

We propose a novel non-structural method for hedging European options, relying on two model-independent results: First, under suitable regularity conditions, an option price can be disentangled into a linear combination of risk-neutral moments. Second, there exists an explicit approximate functional form linking the risk-neutral moments to the futures price of the underlying asset and the related variance swap contracts. We show that S&P 500 call prices are mainly explained by two factors that are related to level and volatility of the underlying index. We empirically compare the performance of two strategies where the vega exposure is adjusted either by a direct position in a variance swap contract or, indirectly, through an at-the-money call. While both strategies ensure effective immunization in periods of market turmoil, taking direct exposure on variance swaps is not optimal during extended periods of subdued volatility.

Suggested Citation

  • Barletta, Andrea & Santucci de Magistris, Paolo & Sloth, David, 2019. "It only takes a few moments to hedge options," Journal of Economic Dynamics and Control, Elsevier, vol. 100(C), pages 251-269.
  • Handle: RePEc:eee:dyncon:v:100:y:2019:i:c:p:251-269
    DOI: 10.1016/j.jedc.2018.11.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165188919300077
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jedc.2018.11.008?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. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
    2. Jondeau, Eric & Rockinger, Michael, 2001. "Gram-Charlier densities," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1457-1483, October.
    3. Harris, David, 1997. "Principal Components Analysis of Cointegrated Time Series," Econometric Theory, Cambridge University Press, vol. 13(4), pages 529-557, February.
    4. Peter Christoffersen & Mathieu Fournier & Kris Jacobs, 2018. "The Factor Structure in Equity Options," The Review of Financial Studies, Society for Financial Studies, vol. 31(2), pages 595-637.
    5. Tebaldi, Claudio, 2005. "Hedging using simulation: a least squares approach," Journal of Economic Dynamics and Control, Elsevier, vol. 29(8), pages 1287-1312, August.
    6. Gondzio, Jacek & Kouwenberg, Roy & Vorst, Ton, 2003. "Hedging options under transaction costs and stochastic volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 1045-1068, April.
    7. Matthias Fengler & Wolfgang Härdle & Christophe Villa, 2003. "The Dynamics of Implied Volatilities: A Common Principal Components Approach," Review of Derivatives Research, Springer, vol. 6(3), pages 179-202, October.
    8. Bates, David S., 2005. "Hedging the smirk," Finance Research Letters, Elsevier, vol. 2(4), pages 195-200, December.
    9. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
    10. 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.
    11. Nicole El Karoui & Monique Jeanblanc‐Picquè & Steven E. Shreve, 1998. "Robustness of the Black and Scholes Formula," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 93-126, April.
    12. Hutchinson, James M & Lo, Andrew W & Poggio, Tomaso, 1994. "A Nonparametric Approach to Pricing and Hedging Derivative Securities via Learning Networks," Journal of Finance, American Finance Association, vol. 49(3), pages 851-889, July.
    13. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 2000. "Pricing and hedging long-term options," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 277-318.
    14. Scott R. Baker & Nicholas Bloom & Steven J. Davis, 2016. "Measuring Economic Policy Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(4), pages 1593-1636.
    15. Rama Cont, 2006. "Model Uncertainty And Its Impact On The Pricing Of Derivative Instruments," Mathematical Finance, Wiley Blackwell, vol. 16(3), pages 519-547, July.
    16. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    17. Coutant, Sophie & Jondeau, Eric & Rockinger, Michael, 2001. "Reading PIBOR futures options smiles: The 1997 snap election," Journal of Banking & Finance, Elsevier, vol. 25(11), pages 1957-1987, November.
    18. Andrea Barletta & Paolo Santucci de Magistris, 2018. "Analyzing the Risks Embedded in Option Prices with rndfittool," Risks, MDPI, vol. 6(2), pages 1-15, March.
    19. Alcock, Jamie & Gray, Philip, 2005. "Dynamic, nonparametric hedging of European style contingent claims using canonical valuation," Finance Research Letters, Elsevier, vol. 2(1), pages 41-50, March.
    20. repec:bla:jfinan:v:53:y:1998:i:6:p:2059-2106 is not listed on IDEAS
    21. 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.
    22. Schneider, Paul, 2015. "Generalized risk premia," Journal of Financial Economics, Elsevier, vol. 116(3), pages 487-504.
    23. Filipović, Damir & Mayerhofer, Eberhard & Schneider, Paul, 2013. "Density approximations for multivariate affine jump-diffusion processes," Journal of Econometrics, Elsevier, vol. 176(2), pages 93-111.
    24. Nicole Branger & Eva Krautheim & Christian Schlag & Norman Seeger, 2012. "Hedging under model misspecification: All risk factors are equal, but some are more equal than others …," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 32(5), pages 397-430, May.
    25. Leif Andersen & Vladimir Piterbarg, 2007. "Moment explosions in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(1), pages 29-50, January.
    26. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31, World Scientific Publishing Co. Pte. Ltd..
    27. Abraham Lioui & Patrice Poncet, 2000. "The Minimum Variance Hedge Ratio Under Stochastic Interest Rates," Management Science, INFORMS, vol. 46(5), pages 658-668, May.
    28. Christoffersen, Peter & Jacobs, Kris, 2004. "The importance of the loss function in option valuation," Journal of Financial Economics, Elsevier, vol. 72(2), pages 291-318, May.
    29. Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, vol. 83(2), pages 413-452, February.
    30. Stutzer, Michael, 1996. "A Simple Nonparametric Approach to Derivative Security Valuation," Journal of Finance, American Finance Association, vol. 51(5), pages 1633-1652, December.
    31. Hansen, Peter R. & Lunde, Asger, 2014. "Estimating The Persistence And The Autocorrelation Function Of A Time Series That Is Measured With Error," Econometric Theory, Cambridge University Press, vol. 30(1), pages 60-93, February.
    32. Hull, John & White, Alan, 2017. "Optimal delta hedging for options," Journal of Banking & Finance, Elsevier, vol. 82(C), pages 180-190.
    33. 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.
    34. Carol Alexander & Andreas Kaeck & Leonardo M. Nogueira, 2009. "Model risk adjusted hedge ratios," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 29(11), pages 1021-1049, November.
    35. Roberto Daluiso & Massimo Morini, 2017. "Hedging efficiently under correlation," Quantitative Finance, Taylor & Francis Journals, vol. 17(10), pages 1535-1547, October.
    36. Rama Cont, 2006. "Model uncertainty and its impact on the pricing of derivative instruments," Post-Print halshs-00002695, HAL.
    37. Branger, Nicole & Mahayni, Antje, 2006. "Tractable hedging: An implementation of robust hedging strategies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(11), pages 1937-1962, November.
    38. Xiu, Dacheng, 2014. "Hermite polynomial based expansion of European option prices," Journal of Econometrics, Elsevier, vol. 179(2), pages 158-177.
    39. Badescu, Alexandru & Elliott, Robert J. & Ortega, Juan-Pablo, 2014. "Quadratic hedging schemes for non-Gaussian GARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 13-32.
    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. Andrea Barletta & Paolo Santucci de Magistris, 2018. "Analyzing the Risks Embedded in Option Prices with rndfittool," Risks, MDPI, vol. 6(2), pages 1-15, March.

    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. 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.
    2. Andrea Barletta & Paolo Santucci de Magistris & Francesco Violante, 2016. "Retrieving Risk-Neutral Densities Embedded in VIX Options: a Non-Structural Approach," CREATES Research Papers 2016-20, Department of Economics and Business Economics, Aarhus University.
    3. 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.
    4. Augustyniak, Maciej & Badescu, Alexandru & Bégin, Jean-François, 2023. "A discrete-time hedging framework with multiple factors and fat tails: On what matters," Journal of Econometrics, Elsevier, vol. 232(2), pages 416-444.
    5. Fengler, Matthias R. & Hin, Lin-Yee, 2015. "Semi-nonparametric estimation of the call-option price surface under strike and time-to-expiry no-arbitrage constraints," Journal of Econometrics, Elsevier, vol. 184(2), pages 242-261.
    6. 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.
    7. Andrea Barletta & Paolo Santucci de Magistris, 2018. "Analyzing the Risks Embedded in Option Prices with rndfittool," Risks, MDPI, vol. 6(2), pages 1-15, March.
    8. Kaeck, Andreas & Seeger, Norman J., 2020. "VIX derivatives, hedging and vol-of-vol risk," European Journal of Operational Research, Elsevier, vol. 283(2), pages 767-782.
    9. Aït-Sahalia, Yacine & Li, Chenxu & Li, Chen Xu, 2021. "Closed-form implied volatility surfaces for stochastic volatility models with jumps," Journal of Econometrics, Elsevier, vol. 222(1), pages 364-392.
    10. Pascal François & Lars Stentoft, 2021. "Smile‐implied hedging with volatility risk," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(8), pages 1220-1240, August.
    11. Fengler, Matthias & Hin, Lin-Yee, 2011. "Semi-nonparametric estimation of the call price surface under strike and time-to-expiry no-arbitrage constraints," Economics Working Paper Series 1136, University of St. Gallen, School of Economics and Political Science, revised May 2013.
    12. Carol Alexander & Andreas Kaeck, 2012. "Does model fit matter for hedging? Evidence from FTSE 100 options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 32(7), pages 609-638, July.
    13. Audrino, Francesco & Fengler, Matthias R., 2015. "Are classical option pricing models consistent with observed option second-order moments? Evidence from high-frequency data," Journal of Banking & Finance, Elsevier, vol. 61(C), pages 46-63.
    14. 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.
    15. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    16. Cosma, Antonio & Galluccio, Stefano & Pederzoli, Paola & Scaillet, Olivier, 2020. "Early Exercise Decision in American Options with Dividends, Stochastic Volatility, and Jumps," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(1), pages 331-356, February.
    17. Jin Zhang & Yi Xiang, 2008. "The implied volatility smirk," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 263-284.
    18. Antonio Cosma & Stefano Galluccio & Paola Pederzoli & O. Scaillet, 2012. "Valuing American Options Using Fast Recursive Projections," Swiss Finance Institute Research Paper Series 12-26, Swiss Finance Institute.
    19. repec:wyi:journl:002108 is not listed on IDEAS
    20. 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.
    21. Jones, Christopher S., 2003. "The dynamics of stochastic volatility: evidence from underlying and options markets," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 181-224.

    More about this item

    Keywords

    Option Greeks; Hedging; Risk-neutral moments; Variance-swap;
    All these keywords.

    JEL classification:

    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    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:dyncon:v:100:y:2019:i:c:p:251-269. 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/jedc .

    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.