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Option pricing for Informed Traders

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  • Stoyan V. Stoyanov
  • Yong Shin Kim
  • Svetlozar T. Rachev
  • Frank J. Fabozzi

Abstract

In this paper we extend the theory of option pricing to take into account and explain the empirical evidence for asset prices such as non-Gaussian returns, long-range dependence, volatility clustering, non-Gaussian copula dependence, as well as theoretical issues such as asymmetric information and the presence of limited arbitrage opportunities

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  • Stoyan V. Stoyanov & Yong Shin Kim & Svetlozar T. Rachev & Frank J. Fabozzi, 2017. "Option pricing for Informed Traders," Papers 1711.09445, arXiv.org.
    • Handle: RePEc:arx:papers:1711.09445
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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Guglielmo Caporale & Luis Gil-Alana, 2014. "Fractional integration and cointegration in US financial time series data," Empirical Economics, Springer, vol. 47(4), pages 1389-1410, December.
    3. Biais, Bruno & Glosten, Larry & Spatt, Chester, 2005. "Market microstructure: A survey of microfoundations, empirical results, and policy implications," Journal of Financial Markets, Elsevier, vol. 8(2), pages 217-264, May.
    4. John Y. Campbell, 2000. "Asset Pricing at the Millennium," Journal of Finance, American Finance Association, vol. 55(4), pages 1515-1567, August.
    5. Harrison, J Michael & Pitbladdo, Richard & Schaefer, Stephen M, 1984. "Continuous Price Processes in Frictionless Markets Have Infinite Variation," The Journal of Business, University of Chicago Press, vol. 57(3), pages 353-365, July.
    6. Søren Johansen, 2010. "An Extension of Cointegration to Fractional Autoregressive Processes," Discussion Papers 10-28, University of Copenhagen. Department of Economics.
    7. Cipian Necula, 2008. "Option Pricing in a Fractional Brownian Motion Environment," Advances in Economic and Financial Research - DOFIN Working Paper Series 2, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
    8. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous‐time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323, October.
    9. Pierre Collin-Dufresne & Vyacheslav Fos, 2015. "Do Prices Reveal the Presence of Informed Trading?," Journal of Finance, American Finance Association, vol. 70(4), pages 1555-1582, August.
    10. Paolo Pasquariello, 2014. "Financial Market Dislocations," The Review of Financial Studies, Society for Financial Studies, vol. 27(6), pages 1868-1914.
    11. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    12. Nielsen, Morten Ørregaard, 2010. "Nonparametric cointegration analysis of fractional systems with unknown integration orders," Journal of Econometrics, Elsevier, vol. 155(2), pages 170-187, April.
    13. Back, Kerry & Pedersen, Hal, 1998. "Long-lived information and intraday patterns," Journal of Financial Markets, Elsevier, vol. 1(3-4), pages 385-402, September.
    14. Robert J. Elliott & John Van Der Hoek, 2003. "A General Fractional White Noise Theory And Applications To Finance," Mathematical Finance, Wiley Blackwell, vol. 13(2), pages 301-330, April.
    15. Tomas Björk & Henrik Hult, 2005. "A note on Wick products and the fractional Black-Scholes model," Finance and Stochastics, Springer, vol. 9(2), pages 197-209, April.
    16. Dwyer, Gerald P, Jr & Locke, Peter R & Yu, Wei, 1996. "Index Arbitrage and Nonlinear Dynamics between the S&P 500 Futures and Cash," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 301-332.
    17. Leland, Hayne E, 1985. "Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    18. Grossman, Sanford J & Stiglitz, Joseph E, 1980. "On the Impossibility of Informationally Efficient Markets," American Economic Review, American Economic Association, vol. 70(3), pages 393-408, June.
    19. Bender, Christian, 2003. "An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter," Stochastic Processes and their Applications, Elsevier, vol. 104(1), pages 81-106, March.
    20. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    21. Friedrich Hubalek & Jan Kallsen & Leszek Krawczyk, 2006. "Variance-optimal hedging for processes with stationary independent increments," Papers math/0607112, arXiv.org.
    22. Craig W. Holden, 1995. "Index arbitrage as cross‐sectional market making," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 15(4), pages 423-455, June.
    23. Erhan Bayraktar & Ulrich Horst & Ronnie Sircar, 2006. "A Limit Theorem for Financial Markets with Inert Investors," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 789-810, November.
    24. Chen, Zhenlong & Xu, Lin & Zhu, Dongjin, 2015. "Generalized continuous time random walks and Hermite processes," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 44-53.
    25. Phillips, Peter C.B., 2007. "Regression With Slowly Varying Regressors And Nonlinear Trends," Econometric Theory, Cambridge University Press, vol. 23(4), pages 557-614, August.
    26. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    27. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    28. Fred Espen Benth, 2003. "On arbitrage-free pricing of weather derivatives based on fractional Brownian motion," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(4), pages 303-324.
    29. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    30. Tommi Sottinen, 2001. "Fractional Brownian motion, random walks and binary market models," Finance and Stochastics, Springer, vol. 5(3), pages 343-355.
    31. Jun Liu, 2004. "Losing Money on Arbitrage: Optimal Dynamic Portfolio Choice in Markets with Arbitrage Opportunities," The Review of Financial Studies, Society for Financial Studies, vol. 17(3), pages 611-641.
    32. 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.
    33. Bryan Kelly & Alexander Ljungqvist, 2012. "Testing Asymmetric-Information Asset Pricing Models," The Review of Financial Studies, Society for Financial Studies, vol. 25(5), pages 1366-1413.
    34. Rostek, Stefan & Schöbel, Rainer, 2006. "Risk preference based option pricing in a fractional Brownian market," Tübinger Diskussionsbeiträge 299, University of Tübingen, School of Business and Economics.
    35. Masahiro Watanabe, 2008. "Price Volatility and Investor Behavior in an Overlapping Generations Model with Information Asymmetry," Journal of Finance, American Finance Association, vol. 63(1), pages 229-272, February.
    36. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    37. Back, Kerry, 1993. "Asymmetric Information and Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 435-472.
    38. Campbell, John Y. & Yogo, Motohiro, 2006. "Efficient tests of stock return predictability," Journal of Financial Economics, Elsevier, vol. 81(1), pages 27-60, July.
    39. Stefan Rostek, 2009. "Option Pricing in Fractional Brownian Markets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-00331-8, February.
    40. Kerry Back & C. Henry Cao & Gregory A. Willard, 2000. "Imperfect Competition among Informed Traders," Journal of Finance, American Finance Association, vol. 55(5), pages 2117-2155, October.
    41. Caporin, Massimiliano & Ranaldo, Angelo & Santucci de Magistris, Paolo, 2013. "On the predictability of stock prices: A case for high and low prices," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5132-5146.
    42. Kim, Y.S. & Stoyanov, S. & Rachev, S. & Fabozzi, F., 2016. "Multi-purpose binomial model: Fitting all moments to the underlying geometric Brownian motion," Economics Letters, Elsevier, vol. 145(C), pages 225-229.
    43. Ball, Clifford A. & Roma, Antonio, 1994. "Stochastic Volatility Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(4), pages 589-607, December.
    44. Brunnermeier, Markus K., 2001. "Asset Pricing under Asymmetric Information: Bubbles, Crashes, Technical Analysis, and Herding," OUP Catalogue, Oxford University Press, number 9780198296980.
    45. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    46. Robert J. Shiller, 2003. "From Efficient Markets Theory to Behavioral Finance," Journal of Economic Perspectives, American Economic Association, vol. 17(1), pages 83-104, Winter.
    47. Davydov, Youri & Rotar, Vladimir, 2008. "On a non-classical invariance principle," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2031-2038, October.
    48. Meerschaert, Mark M. & Scheffler, Hans-Peter, 2008. "Triangular array limits for continuous time random walks," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1606-1633, September.
    49. Pierre Collin-Dufresne & Vyacheslav Fos, 2013. "Do Prices Reveal the Presence of Informed Trading?," Swiss Finance Institute Research Paper Series 13-69, Swiss Finance Institute, revised Sep 2015.
    50. Christian Bender & Robert J. Elliott, 2004. "Arbitrage in a Discrete Version of the Wick-Fractional Black-Scholes Market," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 935-945, November.
    51. Kerry Back & Shmuel Baruch, 2004. "Information in Securities Markets: Kyle Meets Glosten and Milgrom," Econometrica, Econometric Society, vol. 72(2), pages 433-465, March.
    52. 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.
    53. Aase, Knut K. & Bjuland, Terje & Øksendal, Bernt, 2010. "Strategic Insider Trading Equilibrium: A Filter Theory Approach," Discussion Papers 2010/9, Norwegian School of Economics, Department of Business and Management Science.
    54. Francesca Biagini & Paolo Guasoni & Maurizio Pratelli, 2000. "Mean‐Variance Hedging for Stochastic Volatility Models," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 109-123, April.
    55. Christophe Boucher, 2006. "Stock prices–inflation puzzle and the predictability of stock market returns," Post-Print hal-00268110, HAL.
    56. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    57. Xiu, Dacheng, 2014. "Hermite polynomial based expansion of European option prices," Journal of Econometrics, Elsevier, vol. 179(2), pages 158-177.
    58. S. R. Hurst & Eckhard Platen & S. T. Rachev, 1999. "Option pricing for a logstable asset price model," Published Paper Series 1999-2, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    59. Yanyuan Ma & Marc G. Genton, 2000. "Highly Robust Estimation of the Autocovariance Function," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(6), pages 663-684, November.
    60. Lahiri, S. N., 1993. "On the moving block bootstrap under long range dependence," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 405-413, December.
    61. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105, January.
    62. Murad S. Taqqu & Vadim Teverovsky & Walter Willinger, 1999. "Stock market prices and long-range dependence," Finance and Stochastics, Springer, vol. 3(1), pages 1-13.
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