Bid and Ask Asset Pricing Through the Extended Gini Premium Principle: Sufficient and Necessary Conditions for Trading

29 Pages Posted: 8 Nov 2009

See all articles by Luisa Tibiletti

Luisa Tibiletti

University of Turin - Department of Management

Bennet Eisenberg

Lehigh University - Industrial and Systems Engineering Department

Marta Cardin

Ca Foscari University of Venice - Dipartimento di Economia

Date Written: November 6, 2009

Abstract

Since Shalit and Yitzhaki (1984) the premium principle based on the Extended Gini of an uncertain position has been defined as its expected value minus the extended Gini index. We propose this principle for making capital asset pricing tailored to the investor profile. Bid and ask prices of the counter-parties involved in transactions are defined. Risk and gain-premiaare given through "personalized" Extended Gini indices able to capture the buyer risk aversion and the seller gain propension. Sufficient and necessary conditions for trading are set out. Closed-end formulae for the most common asset distributions used in Finance are given and general guide-lines involving the asset skewness drawn. Eventually, we discuss the optimal bid and ask portfolio allocation. We give evidence that if the portfolio distributions are symmetrical and/or the traders have a "moderate" profile the optimal bid-portfolio corresponds always to the worst ask-portfolio. Vice versa, if portfolio distributions are asymmetrical and the traders have an "extreme profile", i.e. strongly risk-averse and highly gain-prone, then optimal bid and ask portfolios are not related.

Keywords: Choquet integral, Distortion functions, Extended Gini Index, Bid and Ask prices, Pessimism and Optimism index, Probability of trading

JEL Classification: G10, G11, G12,G29

Suggested Citation

Tibiletti, Luisa and Eisenberg, Bennet and Cardin, Marta, Bid and Ask Asset Pricing Through the Extended Gini Premium Principle: Sufficient and Necessary Conditions for Trading (November 6, 2009). Available at SSRN: https://ssrn.com/abstract=1501011 or http://dx.doi.org/10.2139/ssrn.1501011

Luisa Tibiletti

University of Turin - Department of Management ( email )

C.so Unione Sovietica, 218 bis
Turin, Turin 10100
Italy
39-11-670-6229 (Phone)
39-11-670-6238 (Fax)

HOME PAGE: http://www.management.unito.it/tibiletti

Bennet Eisenberg

Lehigh University - Industrial and Systems Engineering Department ( email )

Harold S. Mohler Laboratory
200 West Packer Avenue
Bethlehem, PA 18015-1582
United States

Marta Cardin (Contact Author)

Ca Foscari University of Venice - Dipartimento di Economia ( email )

Cannaregio 873
Venice, 30121
Italy

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