Annals of Operations Research

, Volume 262, Issue 2, pp 361–387 | Cite as

On information costs, short sales and the pricing of extendible options, steps and Parisian options

  • Mondher BellalahEmail author
S.I.: Financial Economics


This paper provides a simple framework for the valuation of exotic derivatives within shadow costs of incomplete information and short sales. The specific features of the OTC markets with comparison to the organized markets require an additional investment to obtain information about the financial products, to process data, to elaborate models, etc. The shadow cost includes two components. The first component is the product of pure information cost due to imperfect knowledge. The second component represents the additional cost caused by the short-selling constraint. Information costs are linked to Merton’s (J Fianance 42:483–510, 1987) model of capital market equilibrium with incomplete information, CAPMI. This model is extended by Wu et al. (Rev Quant Finance Account 7:119–136, 1996) who propose incomplete-information capital market equilibrium with heterogeneous expectations and short sale restrictions, GCAPM. This model is used in our paper to provide for the first time in the literature analytic solutions for derivatives in the presence of both shadow costs of incomplete information and short sales. Our methodology incorporates shadow costs of incomplete information and short sales in the options and their underlying securities. We provide formulas using the standard Black and Scholes method or the martingale method. Since shadow costs are important in the presence of illiquidity, the formulas are useful for the valuation of OTC derivatives.


Information costs Short sales Pricing Extendible options Steps options Parisian options 


  1. Bellalah, M. (1999). The valuation of futures and commodity options with information costs. Journal of Futures Markets, 19, 645–664.CrossRefGoogle Scholar
  2. Bellalah, M. (2000). A risk management approach to options trading on the Paris bourse. Derivatives Strategy, 5(6), 31–33.Google Scholar
  3. 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
  4. Bellalah, M., & Wu, Z. (2002). A model for market closure and international portfolio management within incomplete information. International Journal of Theoretical and Applied Finance, 5(5), 479–495.CrossRefGoogle Scholar
  5. 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
  6. Black, F. (1989). How we came up with the option formula. Journal of Portfolio Management, Winter, 15, 4–8.CrossRefGoogle Scholar
  7. Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–659.CrossRefGoogle Scholar
  8. Beltratti, A. (2005). Capital market equilibrium with externalities, production and heterogeneous agents. Journal of Banking & Finance, 29, 3061–3073.CrossRefGoogle Scholar
  9. 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
  10. Chesney, M., Jeanblanc-Pique, M., & Yor, M. (1995). Brownian excursions and Parisian barrier options. Journal of Applied Probability, 29, 165–184.CrossRefGoogle Scholar
  11. Harrison, J. M., & Kreps, D. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20, 381–408.CrossRefGoogle Scholar
  12. Harrison, J. M., & Pliska, S. (1981). Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes and Their Applications, 11, 215–260.CrossRefGoogle Scholar
  13. Linetsky, V. (1999). Step options. Mathematical Finance, 9, 55–96.CrossRefGoogle Scholar
  14. Mackowiak, B., & Wiederholt, M. (2012). Information processing and limited liability. American Economic Review, 102(3), 30–34.CrossRefGoogle Scholar
  15. Merton, R. C. (1987). A simple model of capital market equilibrium with incomplete information. Journal of Finance, 42, 483–510.CrossRefGoogle Scholar
  16. Merton, R. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science, 4, 141–183.CrossRefGoogle Scholar
  17. Merton, R. C. (1998). Applications of option pricing theory: Twenty-five years later. American Economic Review, N2, 323–348.Google Scholar
  18. Nezafat, M., & Wang, Q. (2013). Short-sale constraints, information acquisition, and asset orices. August, Scheller College of Business, Georgia Institute of Technology, Atlanta, GA 30308.Google Scholar
  19. Rubinstein, M., & Reiner, E. (1991). Breaking down the barriers. Risk, 4, 28–35.Google Scholar
  20. Van Nieuwerburgh, S., & Veldkamp, S. (2009). Information immobility and the home bias puzzle. Journal of Finance, 64(3), 1187–1215.CrossRefGoogle Scholar
  21. Van Nieuwerburgh, S., & Veldkamp, L. (2010). Information acquisition and under-diversification. Review of Economic Studies, 77(2), 779–805.CrossRefGoogle Scholar
  22. Verona, F. (2013). Investment dynamics with information costs (Vol. 18). Bank of Finland Research, Discussion Papers.Google Scholar
  23. Wu, C., Li, Q., & John Wei, K. C. (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 2015

Authors and Affiliations

  1. 1.Universite de Cergy-PontoiseCergy-PontoiseFrance

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