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Endogenous Collateral: Arbitrage and Equilibrium without Bounded Short Sales

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

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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Paper provided by Finance Lab, Insper Instituto de Ensino e Pesquisa in its series Finance Lab Working Papers with number flwp_52.

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Date of creation: Oct 2003
Date of revision:
Handle: RePEc:ibm:finlab:flwp_52
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  1. Aloisio Araújo & Jaime Orrillo & Mario R. Páscoa, 2000. "Equilibrium with Default and Endogenous Collateral," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 1-21.
  2. 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.
  3. Fajardo, J., 2004. "A Note On Arbitrage and Exogenus Collateral," Finance Lab Working Papers flwp_62, Finance Lab, Insper Instituto de Ensino e Pesquisa.
  4. Araujo, A. & Monteiro, P. K. & Páscoa, M.R., . "Incomplete markets, continuum of states and default," CORE Discussion Papers RP 1297, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Donald A. Walker (ed.), 2000. "Equilibrium," Books, Edward Elgar Publishing, volume 0, number 1585, 10.
  6. 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.
  7. Elyégs Jouini & Hédi Kallal, 1995. "Arbitrage In Securities Markets With Short-Sales Constraints," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 197-232.
  8. John Geanakoplos & Pradeep Dubey, 1989. "Liquidity and Bankruptcy with Incomplete Markets: Pure Exchange," Cowles Foundation Discussion Papers 900, Cowles Foundation for Research in Economics, Yale University.
  9. 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.
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