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

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  • Mondher Bellalah

    (Universite de Cergy-Pontoise)

Abstract

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.

Suggested Citation

  • Mondher Bellalah, 2018. "On information costs, short sales and the pricing of extendible options, steps and Parisian options," Annals of Operations Research, Springer, vol. 262(2), pages 361-387, March.
    • Handle: RePEc:spr:annopr:v:262:y:2018:i:2:d:10.1007_s10479-015-2050-y
    DOI: 10.1007/s10479-015-2050-y
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    References listed on IDEAS

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    1. Mondher Bellalah, 1999. "Valuation of futures and commodity options with information costs," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 19(6), pages 645-664, September.
    2. Mondher Bellalah & Zhen Wu, 2009. "A simple model of corporate international investment under incomplete information and taxes," Annals of Operations Research, Springer, vol. 165(1), pages 123-143, January.
    3. Stijn Van Nieuwerburgh & Laura Veldkamp, 2009. "Information Immobility and the Home Bias Puzzle," Journal of Finance, American Finance Association, vol. 64(3), pages 1187-1215, June.
    4. Bartosz Mackowiak & Mirko Wiederholt, 2012. "Information Processing and Limited Liability," American Economic Review, American Economic Association, vol. 102(3), pages 30-34, May.
    5. Merton, Robert C, 1987. "A Simple Model of Capital Market Equilibrium with Incomplete Information," Journal of Finance, American Finance Association, vol. 42(3), pages 483-510, July.
    6. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    7. Robert Battalio & Paul Schultz, 2011. "Regulatory Uncertainty and Market Liquidity: The 2008 Short Sale Ban's Impact on Equity Option Markets," Journal of Finance, American Finance Association, vol. 66(6), pages 2013-2053, December.
    8. Merton, Robert C, 1998. "Applications of Option-Pricing Theory: Twenty-Five Years Later," American Economic Review, American Economic Association, vol. 88(3), pages 323-349, June.
    9. Wu, Chunchi & Li, Qiang & Weii, K C John, 1996. "Incomplete-Information Capital Market Equilibrium with Heterogeneous Expectations and Short Sale Restrictions," Review of Quantitative Finance and Accounting, Springer, vol. 7(2), pages 119-136, September.
    10. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    11. Fabio Verona, 2014. "Investment Dynamics with Information Costs," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 46(8), pages 1627-1656, December.
    12. Beltratti, Andrea, 2005. "Capital market equilibrium with externalities, production and heterogeneous agents," Journal of Banking & Finance, Elsevier, vol. 29(12), pages 3061-3073, December.
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    14. Stijn Van Nieuwerburgh & Laura Veldkamp, 2010. "Information Acquisition and Under-Diversification," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(2), pages 779-805.
    15. 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..
    16. Mondher Bellalah & Zhen Wu, 2002. "A Model For Market Closure And International Portfolio Management Within Incomplete Information," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(05), pages 479-495.
    17. 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.
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    Cited by:

    1. Mondher Bellalah & Yaosheng Xu & Detao Zhang, 2019. "Intertemporal optimal portfolio choice based on labor income within shadow costs of incomplete information and short sales," Annals of Operations Research, Springer, vol. 281(1), pages 397-422, October.

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