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Endogenous Collateral: Arbitrage and Equilibrium without Bounded Short Sales

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  • Araujo, A.
  • Fajardo, J
  • Páscoa, M. R.

Abstract

We study the implications of the absence of arbitrage in an two period economy where default is allowed and assets are secured by collateral choosen by the borrowers. We show that non arbitrage sale prices of assets are submartingales, whereas non arbitrage purchase prices of the derivatives (secured by the pool of collaterals) are supermartingales. We use these non arbitrage conditions to establish existence of equilibrium, without imposing bounds on short sales. The nonconvexity of the budget set is overcome by considering a continuum of agents. Our results are particularly relevant for the collateralized mortgage obligations(CMO) markets.
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Suggested Citation

  • Araujo, A. & Fajardo, J & Páscoa, M. R., 2003. "Endogenous Collateral: Arbitrage and Equilibrium without Bounded Short Sales," Finance Lab Working Papers flwp_52, Finance Lab, Insper Instituto de Ensino e Pesquisa.
    • Handle: RePEc:ibm:finlab:flwp_52
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    References listed on IDEAS

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    1. A. Araujo & M. R. Páscoa & P. K. Monteiro, 1997. "Incomplete markets, continuum of states and default," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 205-213.
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    3. Magill, Michael & Shafer, Wayne, 1991. "Incomplete markets," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 30, pages 1523-1614, Elsevier.
    4. Hart, Oliver D., 1975. "On the optimality of equilibrium when the market structure is incomplete," Journal of Economic Theory, Elsevier, vol. 11(3), pages 418-443, December.
    5. Fajardo, Jose, 2005. "A note on arbitrage and exogenous collateral," Mathematical Social Sciences, Elsevier, vol. 50(3), pages 336-341, November.
    6. Elyégs Jouini & Hédi Kallal, 1995. "Arbitrage In Securities Markets With Short‐Sales Constraints," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 197-232, July.
    7. Aloisio Araujo & Paulo K. Monteiro & M´rio Rui P´ascoa, 1996. "Infinite Horizon Incomplete Markets With A Continuum Of States," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 119-132, April.
    8. Duffie, Darrell & Shafer, Wayne, 1985. "Equilibrium in incomplete markets: I : A basic model of generic existence," Journal of Mathematical Economics, Elsevier, vol. 14(3), pages 285-300, June.
    9. Donald A. Walker (ed.), 2000. "Equilibrium," Books, Edward Elgar Publishing, volume 0, number 1585.
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