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It only takes a few moments to hedge options

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  • 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
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    as
    1. Jondeau, Eric & Rockinger, Michael, 2001. "Gram-Charlier densities," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1457-1483, October.
    2. Tebaldi, Claudio, 2005. "Hedging using simulation: a least squares approach," Journal of Economic Dynamics and Control, Elsevier, vol. 29(8), pages 1287-1312, August.
    3. 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.
    4. Bates, David S., 2005. "Hedging the smirk," Finance Research Letters, Elsevier, vol. 2(4), pages 195-200, December.
    5. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Leif Andersen & Vladimir Piterbarg, 2007. "Moment explosions in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(1), pages 29-50, January.
    15. 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..
    16. Abraham Lioui & Patrice Poncet, 2000. "The Minimum Variance Hedge Ratio Under Stochastic Interest Rates," Management Science, INFORMS, vol. 46(5), pages 658-668, May.
    17. 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.
    18. 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.
    19. 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.
    20. Stutzer, Michael, 1996. "A Simple Nonparametric Approach to Derivative Security Valuation," Journal of Finance, American Finance Association, vol. 51(5), pages 1633-1652, December.
    21. 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.
    22. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 2000. "Pricing and hedging long-term options," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 277-318.
    23. 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.
    24. 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.
    25. 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.
    26. Xiu, Dacheng, 2014. "Hermite polynomial based expansion of European option prices," Journal of Econometrics, Elsevier, vol. 179(2), pages 158-177.
    27. 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.
    28. Harris, David, 1997. "Principal Components Analysis of Cointegrated Time Series," Econometric Theory, Cambridge University Press, vol. 13(4), pages 529-557, February.
    29. 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.
    30. 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.
    31. 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.
    32. 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.
    33. 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.
    34. repec:bla:jfinan:v:53:y:1998:i:6:p:2059-2106 is not listed on IDEAS
    35. Schneider, Paul, 2015. "Generalized risk premia," Journal of Financial Economics, Elsevier, vol. 116(3), pages 487-504.
    36. 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.
    37. Hull, John & White, Alan, 2017. "Optimal delta hedging for options," Journal of Banking & Finance, Elsevier, vol. 82(C), pages 180-190.
    38. Roberto Daluiso & Massimo Morini, 2017. "Hedging efficiently under correlation," Quantitative Finance, Taylor & Francis Journals, vol. 17(10), pages 1535-1547, October.
    39. Rama Cont, 2006. "Model uncertainty and its impact on the pricing of derivative instruments," Post-Print halshs-00002695, HAL.
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    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.

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    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

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