IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v69y2021i1p100-113.html
   My bibliography  Save this article

Risk Arbitrage Opportunities for Stock Index Options

Author

Listed:
  • Thierry Post

    (Graduate School of Business, Nazarbayev University, Astana 01000, Kazakhstan, Department of Economic Modeling, National Analytical Center ‘Analytica,’ Astana 01000, Kazakhstan)

  • Iňaki Rodríguez Longarela

    (Department of Finance, Stockholm Business School, Stockholm University, 106 91 Stockholm, Sweden)

Abstract

To analyze the economic significance of pricing errors of stock index options, a system of linear inequalities is developed that completely characterizes all risk arbitrage opportunities that arise if a well-behaved pricing kernel does not exist. The stochastic arbitrage system can account for market imperfections in the form of transactions costs and general portfolio restrictions. An active trading strategy based on the stochastic arbitrage system for front-month S&P500 stock index options yields significant abnormal returns out of sample for small-scale portfolios. However, outperformance seems elusive if the strategy is scaled up and market depth is taken into account.

Suggested Citation

  • Thierry Post & Iňaki Rodríguez Longarela, 2021. "Risk Arbitrage Opportunities for Stock Index Options," Operations Research, INFORMS, vol. 69(1), pages 100-113, January.
    • Handle: RePEc:inm:oropre:v:69:y:2021:i:1:p:100-113
    DOI: 10.1287/opre.2020.2012
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/opre.2020.2012
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.2020.2012?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. Almeida, Caio & Garcia, René, 2012. "Assessing misspecified asset pricing models with empirical likelihood estimators," Journal of Econometrics, Elsevier, vol. 170(2), pages 519-537.
    2. Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
    3. Christian Julliard & Anisha Ghosh, 2012. "Can Rare Events Explain the Equity Premium Puzzle?," The Review of Financial Studies, Society for Financial Studies, vol. 25(10), pages 3037-3076.
    4. Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Whang, 2005. "Consistent Testing for Stochastic Dominance under General Sampling Schemes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 735-765.
    5. Iñaki R. Longarela, 2016. "A Characterization of the SSD-Efficient Frontier of Portfolio Weights by Means of a Set of Mixed-Integer Linear Constraints," Management Science, INFORMS, vol. 62(12), pages 3549-3554, December.
    6. Oliver Linton & Thierry Post & Yoon‐Jae Whang, 2014. "Testing for the stochastic dominance efficiency of a given portfolio," Econometrics Journal, Royal Economic Society, vol. 17(2), pages 59-74, June.
    7. Hansen, Lars Peter & Jagannathan, Ravi, 1991. "Implications of Security Market Data for Models of Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 225-262, April.
    8. Dmitriy Muravyev & Neil D Pearson & Stijn Van Nieuwerburgh, 2020. "Options Trading Costs Are Lower than You Think," The Review of Financial Studies, Society for Financial Studies, vol. 33(11), pages 4973-5014.
    9. Russell Davidson & Jean-Yves Duclos, 2013. "Testing for Restricted Stochastic Dominance," Econometric Reviews, Taylor & Francis Journals, vol. 32(1), pages 84-125, January.
    10. Faias, José Afonso & Santa-Clara, Pedro, 2017. "Optimal Option Portfolio Strategies: Deepening the Puzzle of Index Option Mispricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 52(1), pages 277-303, February.
    11. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-126, March.
    12. Dybvig, Philip H, 1988. "Distributional Analysis of Portfolio Choice," The Journal of Business, University of Chicago Press, vol. 61(3), pages 369-393, July.
    13. repec:bla:jfinan:v:43:y:1988:i:2:p:301-08 is not listed on IDEAS
    14. Caio Almeida & René Garcia, 2017. "Economic Implications of Nonlinear Pricing Kernels," Management Science, INFORMS, vol. 63(10), pages 3361-3380, October.
    15. George M. Constantinides & Michal Czerwonko & Stylianos Perrakis, 2020. "Mispriced index option portfolios," Financial Management, Financial Management Association International, vol. 49(2), pages 297-330, June.
    16. George M. Constantinides & Michal Czerwonko & Jens Carsten Jackwerth & Stylianos Perrakis, 2011. "Are Options on Index Futures Profitable for Risk‐Averse Investors? Empirical Evidence," Journal of Finance, American Finance Association, vol. 66(4), pages 1407-1437, August.
    17. repec:bla:jfinan:v:58:y:2003:i:5:p:1905-1932 is not listed on IDEAS
    18. Beare, Brendan K., 2011. "Measure preserving derivatives and the pricing kernel puzzle," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 689-697.
    19. Yuichi Kitamura & Gautam Tripathi & Hyungtaik Ahn, 2004. "Empirical Likelihood-Based Inference in Conditional Moment Restriction Models," Econometrica, Econometric Society, vol. 72(6), pages 1667-1714, November.
    20. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1683, August.
    21. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    22. Russell Davidson, 2009. "Testing for Restricted Stochastic Dominance: Some Further Results," Review of Economic Analysis, Digital Initiatives at the University of Waterloo Library, vol. 1(1), pages 34-59, September.
    23. Levy, Haim, 1985. "Upper and Lower Bounds of Put and Call Option Value: Stochastic Dominance Approach," Journal of Finance, American Finance Association, vol. 40(4), pages 1197-1217, September.
    24. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 335-346.
    25. Perrakis, Stylianos, 1986. "Option Bounds in Discrete Time: Extensions and the Pricing of the American Put," The Journal of Business, University of Chicago Press, vol. 59(1), pages 119-141, January.
    26. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    27. Anisha Ghosh & Christian Julliard & Alex P. Taylor, 2017. "What Is the Consumption-CAPM Missing? An Information-Theoretic Framework for the Analysis of Asset Pricing Models," The Review of Financial Studies, Society for Financial Studies, vol. 30(2), pages 442-504.
    28. Thierry Post, 2003. "Empirical Tests for Stochastic Dominance Efficiency," Journal of Finance, American Finance Association, vol. 58(5), pages 1905-1931, October.
    29. Victor DeMiguel & Lorenzo Garlappi & Francisco J. Nogales & Raman Uppal, 2009. "A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms," Management Science, INFORMS, vol. 55(5), pages 798-812, May.
    30. Constantinides, George M. & Perrakis, Stylianos, 2002. "Stochastic dominance bounds on derivatives prices in a multiperiod economy with proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1323-1352, July.
    31. Perrakis, Stylianos & Ryan, Peter J, 1984. "Option Pricing Bounds in Discrete Time," Journal of Finance, American Finance Association, vol. 39(2), pages 519-525, June.
    32. Moshe Leshno & Haim Levy, 2002. "Preferred by "All" and Preferred by "Most" Decision Makers: Almost Stochastic Dominance," Management Science, INFORMS, vol. 48(8), pages 1074-1085, August.
    33. repec:bla:jfinan:v:58:y:2003:i:4:p:1651-1684 is not listed on IDEAS
    34. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    35. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    36. Ritchken, Peter H, 1985. "On Option Pricing Bounds," Journal of Finance, American Finance Association, vol. 40(4), pages 1219-1233, September.
    37. Thierry Post & Valerio Potì, 2017. "Portfolio Analysis Using Stochastic Dominance, Relative Entropy, and Empirical Likelihood," Management Science, INFORMS, vol. 63(1), pages 153-165, January.
    38. Oliver Linton & Thierry Post & Yoon‐Jae Whang, 2014. "Testing for the stochastic dominance efficiency of a given portfolio," Econometrics Journal, Royal Economic Society, vol. 17(2), pages 59-74, June.
    39. Kroll, Yoram & Levy, Haim, 1980. "Sampling Errors and Portfolio Efficient Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(3), pages 655-688, September.
    40. Peter Ritchken & Shyanjaw Kuo, 1989. "On Stochastic Dominance and Decreasing Absolute Risk Averse Option Pricing Bounds," Management Science, INFORMS, vol. 35(1), pages 51-59, January.
    41. Timo Kuosmanen, 2004. "Efficient Diversification According to Stochastic Dominance Criteria," Management Science, INFORMS, vol. 50(10), pages 1390-1406, October.
    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. Brendan K. Beare, 2023. "Optimal measure preserving derivatives revisited," Mathematical Finance, Wiley Blackwell, vol. 33(2), pages 370-388, April.
    2. Armstrong, John & Brigo, Damiano, 2022. "Coherent risk measures alone are ineffective in constraining portfolio losses," Journal of Banking & Finance, Elsevier, vol. 140(C).
    3. Fang, Yi & Post, Thierry, 2022. "Optimal portfolio choice for higher-order risk averters," Journal of Banking & Finance, Elsevier, vol. 137(C).
    4. Conlon, Thomas & Cotter, John & Kovalenko, Illia & Post, Thierry, 2023. "A financial modeling approach to industry exchange-traded funds selection," Journal of Empirical Finance, Elsevier, vol. 74(C).
    5. Brendan K. Beare & Juwon Seo & Zhongxi Zheng, 2022. "Stochastic arbitrage with market index options," Papers 2207.00949, arXiv.org, revised May 2024.

    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. Post, Thierry & Karabatı, Selçuk & Arvanitis, Stelios, 2018. "Portfolio optimization based on stochastic dominance and empirical likelihood," Journal of Econometrics, Elsevier, vol. 206(1), pages 167-186.
    2. Stelios Arvanitis & Thierry Post & Nikolas Topaloglou, 2021. "Stochastic Bounds for Reference Sets in Portfolio Analysis," Management Science, INFORMS, vol. 67(12), pages 7737-7754, December.
    3. Brendan K. Beare & Juwon Seo & Zhongxi Zheng, 2022. "Stochastic arbitrage with market index options," Papers 2207.00949, arXiv.org, revised May 2024.
    4. Stylianos Perrakis, 2022. "From innovation to obfuscation: continuous time finance fifty years later," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 36(3), pages 369-401, September.
    5. Kolokolova, Olga & Le Courtois, Olivier & Xu, Xia, 2022. "Is the index efficient? A worldwide tour with stochastic dominance," Journal of Financial Markets, Elsevier, vol. 59(PB).
    6. George M. Constantinides & Michal Czerwonko & Stylianos Perrakis, 2020. "Mispriced index option portfolios," Financial Management, Financial Management Association International, vol. 49(2), pages 297-330, June.
    7. Duc Khuong Nguyen & Nikolas Topaloglou & Thomas Walther, 2020. "Asset Classes and Portfolio Diversification: Evidence from a Stochastic Spanning Approach," Working Papers 2020-009, Department of Research, Ipag Business School.
    8. Liesiö, Juuso & Xu, Peng & Kuosmanen, Timo, 2020. "Portfolio diversification based on stochastic dominance under incomplete probability information," European Journal of Operational Research, Elsevier, vol. 286(2), pages 755-768.
    9. Arvanitis, Stelios & Post, Thierry & Potì, Valerio & Karabati, Selcuk, 2021. "Nonparametric tests for Optimal Predictive Ability," International Journal of Forecasting, Elsevier, vol. 37(2), pages 881-898.
    10. Thierry Post & Miloš Kopa, 2017. "Portfolio Choice Based on Third-Degree Stochastic Dominance," Management Science, INFORMS, vol. 63(10), pages 3381-3392, October.
    11. Arvanitis, Stelios & Scaillet, Olivier & Topaloglou, Nikolas, 2020. "Spanning tests for Markowitz stochastic dominance," Journal of Econometrics, Elsevier, vol. 217(2), pages 291-311.
    12. 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.
    13. Thierry Post & Valerio Potì, 2017. "Portfolio Analysis Using Stochastic Dominance, Relative Entropy, and Empirical Likelihood," Management Science, INFORMS, vol. 63(1), pages 153-165, January.
    14. Hamed Ghanbari & Michael Oancea & Stylianos Perrakis, 2021. "Shedding light on a dark matter: Jump diffusion and option‐implied investor preferences," European Financial Management, European Financial Management Association, vol. 27(2), pages 244-286, March.
    15. Constantinides, George M. & Jackwerth, Jens Carsten & Perrakis, Stylianos, 2005. "Option pricing: Real and risk-neutral distributions," CoFE Discussion Papers 05/06, University of Konstanz, Center of Finance and Econometrics (CoFE).
    16. Arvanitis, Stelios & Scaillet, Olivier & Topaloglou, Nikolas, 2020. "Spanning analysis of stock market anomalies under prospect stochastic dominance," Working Papers unige:134101, University of Geneva, Geneva School of Economics and Management.
    17. Hildebrandt, Patrick & Knoke, Thomas, 2011. "Investment decisions under uncertainty--A methodological review on forest science studies," Forest Policy and Economics, Elsevier, vol. 13(1), pages 1-15, January.
    18. Christodoulakis, George & Mohamed, Abdulkadir & Topaloglou, Nikolas, 2018. "Optimal privatization portfolios in the presence of arbitrary risk aversion," European Journal of Operational Research, Elsevier, vol. 265(3), pages 1172-1191.
    19. Fang, Yi & Post, Thierry, 2017. "Higher-degree stochastic dominance optimality and efficiency," European Journal of Operational Research, Elsevier, vol. 261(3), pages 984-993.
    20. Kallio, Markku & Dehghan Hardoroudi, Nasim, 2018. "Second-order stochastic dominance constrained portfolio optimization: Theory and computational tests," European Journal of Operational Research, Elsevier, vol. 264(2), pages 675-685.

    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:inm:oropre:v:69:y:2021:i:1:p:100-113. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.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.