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Annals of Operations Research

, Volume 262, Issue 2, pp 389–411 | Cite as

Pricing derivatives in the presence of shadow costs of incomplete information and short sales

  • Mondher bellalahEmail author
S.I.: Financial Economics

Abstract

Financial models are based on the standard assumptions of frictionless markets, complete information, no transaction costs and no taxes and borrowing and short selling without restrictions. Merton’s (J Finance 42:483–510, 1987) develops a simple model of capital market equilibrium with incomplete information. Wu et al. (Rev Quant Finance Account 7:119–136, 1996) extend Merton’s (J Finance 42:483–510, 1987) model by proposing an incomplete information capital market equilibrium with heterogeneous expectations and short sale restrictions, GCAPM. The shadow costs include two components. The first component is the product of pure information cost due to imperfect knowledge and heterogeneous expectations. The second component represents the additional cost caused by the short-selling constraint. Short-selling bans around the world after the global financial crisis become more and more important. Nezafat and Wang (Short-sale constraints, information acquisition, and asset prices, Scheller College of Business, Georgia Institute of Technology, Atlanta, p 30308, 2013) develop a model of information acquisition and portfolio choice under short-sale constraints. Bellalah (J Futures Mark, 1999) and Bellalah and Wu (Ann Oper Res 165:123–143, 2009) include information costs the valuation of assets and derivatives. This is the first study to our knowledge devoted to the pricing of derivatives that accounts simultaneously for information costs and short sales constraints for the option market and its underlying asset market. We extend the classic models by Black and Scholes (J Polit Econ 81:637–659, 1973), Black (J Financ Econ 79(3):167–179, 1976), and Barone-Adesi and Whaley (J Finance 2(81):303–320, 1987) among others to account for shadow costs of incomplete information and short sales. We present a general method and provide the general differential equation for the pricing of derivatives within incomplete information and short selling costs.

Keywords

Pricing Incomplete information Differential equation Derivatives Information costs Short sales costs 

JEL Classification

G3 G31 G32 G33 

References

  1. Barone-Adesi, G., & Whaley, R. E. (1987). Efficient analytic approximation of American option values. Journal of Finance, 2(81), 303–320.Google Scholar
  2. Battalio, R., & Schultz, P. (2011). Regulatory uncertainty and market liquidity: The 2008 short sale ban’s impact on equity option markets. Journal of Finance, 66(6), 2013–2053.CrossRefGoogle Scholar
  3. Beber, A., & Pagano, M. (2013). Short-selling bans around the world: Evidence from the 2007–2009 crisis. Journal of Finance, 68(1), 343–381.CrossRefGoogle Scholar
  4. Bellalah, M. (1999). The valuation of futures and commodity options with information costs. Journal of Futures Markets, 19, 645–664.CrossRefGoogle Scholar
  5. Bellalah, M. (2000). Valuation of American CAC 40 index and wild card options. International Review of Economics and Finance, 10, 75–94.CrossRefGoogle Scholar
  6. Bellalah, M. (2001). Market imperfections, information costs and the valuation of derivatives: Some general results. International Journal of Finance, 13(3), 1895–1927.Google Scholar
  7. Bellalah, M., & Wu, Z. (2009). A simple model of corporate international investment under incomplete information and taxes. Annals of Operations Research, 165, 123–143.CrossRefGoogle Scholar
  8. Beltratti, A. (2005). Capital market equilibrium with externalities, production and heterogeneous agents. Journal of Banking & Finance, 29(2005), 3061–3073.CrossRefGoogle Scholar
  9. Black, F. (1976). The pricing of commodity contracts. Journal of Financial Economics, 79(3), 167–179.CrossRefGoogle Scholar
  10. Black, F. (1989). How we came up with the option formula. Journal of Portfolio Management, 15, 4–8.CrossRefGoogle Scholar
  11. Black, F., & Scholes, M. (1973). The pricing of options and corporate Liabilities. Journal of Political Economy, 81, 637–659.CrossRefGoogle Scholar
  12. Boehmer, E., Jones, C. M., & Zhang, X. (2013). Shackling short sellers: The 2008 shorting ban. Review of Financial Studies, 26, 287–322.CrossRefGoogle Scholar
  13. Boehmer, E., Jones, C.M., & Zhang, X. (forthcoming). Shackling short sellers: The 2008 shorting ban. Review of Financial Studies.Google Scholar
  14. Boehmer, E., & Wu, J. (2013). Short selling and the price discovery process. Review of Financial Studies, 26(2), 287–322.CrossRefGoogle Scholar
  15. Bris, A., Goetzmann, W. N., & Zhu, N. (2007). Efficiency and the bear: Short sales and markets around the world. Journal of Finance, 62(3), 1029–1079.CrossRefGoogle Scholar
  16. Cabrales, A., Gossner, O., & Serrano, R. (2013). Entropy and the value of information for investors. American Economic Review, 103(1), 360–377.CrossRefGoogle Scholar
  17. Cao, H. H. (1999). The effect of derivative assets on information acquisition and price behavior in a rational expectations equilibrium. Review of Financial Studies, 12(1), 131–163.CrossRefGoogle Scholar
  18. Cao, H. H., Zhang, H. H., & Zhou, X. (2007). Short-sale constraint, informational efficiency, and asset price bias. Working paper. University of Texas-Dallas.Google Scholar
  19. Cox, J. C., Ingersoll, J. E., & Ross, S. A. (1985). A theory of the term structure of interest rates. Econometrica, 53, 385–407.CrossRefGoogle Scholar
  20. Garman, M. (1976). A general theory of asset valuation under diffusion state processes, W.P. N 50. Berkeley: University of California.Google Scholar
  21. Garman, M., & Kohlhagen, S. (1983). Foreign currency option values. Journal of International Money and Finance, 2, 231–237.CrossRefGoogle Scholar
  22. Lintner, J. (1965). Security prices, risk and maximal gains from diversification. Journal of Finance, 20, 587–516.Google Scholar
  23. Mackowiak, B., & Wiederholt, M. (2012). Information processing and limited liability. American Economic Review, 102(3), 30–34.CrossRefGoogle Scholar
  24. Markowitz, H. M. (1952). Portfolio selection. Journal of Finance, 7(1), 77–91.Google Scholar
  25. Massa, M. (2002). Financial innovation and information: The role of derivatives when a market for information exists. Review of Financial Studies, 15(3), 927–957.CrossRefGoogle Scholar
  26. Merton, R. C. (1987). A simple model of capital market equilibrium with incomplete information. Journal of Finance, 42, 483–510.CrossRefGoogle Scholar
  27. Merton, R. C. (1998). Applications of option pricing theory: Twenty-five years later. American Economic Review, 2, 323–348.Google Scholar
  28. Miller, M. (1988). The Modigliani-Miller propositions after thirty years. Journal of Economic Perspectives, 2, 99–120.CrossRefGoogle Scholar
  29. Nezafat, M., & Wang, Q. (2013). Short-sale constraints, information acquisition, and asset prices (p. 30308). Atlanta, GA: Scheller College of Business, Georgia Institute of Technology.Google Scholar
  30. Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance, 19, 425–442.Google Scholar
  31. Van Nieuwerburgh, S., & Veldkamp, L. (2009). Information immobility and the home bias puzzle. Journal of Finance, 64(3), 1187–1215.CrossRefGoogle Scholar
  32. Van Nieuwerburgh, S., & Veldkamp, L. (2010). Information acquisition and under-diversification. Review of Economic Studies, 77(2), 779–805.CrossRefGoogle Scholar
  33. Verona, F. (2013). Investment dynamics with information costs. Discussion Papers: Bank of Finland Research. 18.Google Scholar
  34. Winkelmann, S. (2013). Markov decision processes with information costs: Theory and application, Dissertation: Fachbereich mathematik und informatik. Freie Universität Berlin April 2013.Google Scholar
  35. Wu, C., Li, Q., & Wei, K. C. J. (1996). Incomplete information capital market equilibrium with heteregeonous expectations and short sale restrictions. Review of Quantitative Finance and Accounting, 7, 119–136.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.THEMAUniversity de CergyCergyFrance

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