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


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.


Pricing Incomplete information Differential equation Derivatives Information costs Short sales costs 

JEL Classification

G3 G31 G32 G33 


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.THEMAUniversity de CergyCergyFrance

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