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Dry Markets and Superreplication Bounds of American Derivatives

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Author Info
Matos, Joao Amaro de
Lacerda, Ana

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Abstract

This paper studies the impact of dry markets for underlying assets on the pricing of American derivatives, using a disrete time framework. Dry markets are characterized by the possibility of non-existence of trading at certain dates. Such non-existence may be deterministic or probabilistic. Using superreplicating strategies, we derive expectation representations for the range of arbitrage-free values of the dervatives. In the probabilistic case, if we consider an enlarged filtration induced by the price process and the market existence process, ordinary stopping times are required. If not, randomized stopping times are required. Several comparisons of the ranges obtained with the two market restrictions are performed. Finally, we conclude that arbitrage arguments are not enough to define the optimal exercise policy.

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Publisher Info
Paper provided by Universidade Nova de Lisboa, Faculdade de Economia in its series FEUNL Working Paper Series with number wp461.

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Length: 51 pages
Date of creation: 2004
Date of revision:
Handle: RePEc:unl:unlfep:wp461

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Related research
Keywords: American derivatives; pricing; incomplete markets; dry markets; superreplication; randomized stopping times; strong duality;

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References listed on IDEAS
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  1. 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. [Downloadable!] (restricted)
  2. H. Föllmer & D. Kramkov, . "Optional decompositions under constraints," Sonderforschungsbereich 373 1997-31, Humboldt Universitaet Berlin.
  3. Prasad Chalasani & Somesh Jha, 2001. "Randomized Stopping Times and American Option Pricing with Transaction Costs," Mathematical Finance, Blackwell Publishing, vol. 11(1), pages 33-77. [Downloadable!] (restricted)
  4. Ioannis Karatzas & (*), S. G. Kou, 1998. "Hedging American contingent claims with constrained portfolios," Finance and Stochastics, Springer, vol. 2(3), pages 215-258. [Downloadable!] (restricted)
  5. Longstaff, Francis A, 2001. "Optimal Portfolio Choice and the Valuation of Illiquid Securities," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 14(2), pages 407-31.
  6. João Amaro de Matos & Paula Antão, 2001. "Super-replicating Bounds on European Option Prices when the Underlying Asset is Illiquid," Economics Bulletin, Economics Bulletin, vol. 7, pages 1-7. [Downloadable!]
  7. John H. Cochrane & Jesus Saa-Requejo, 1996. "Beyond Arbitrage: "Good-Deal" Asset Price Bounds in Incomplete Markets," NBER Working Papers 5489, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  8. Kramkov, D.O., 1994. "Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets," Discussion Paper Serie B 294, University of Bonn, Germany. [Downloadable!]
  9. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 6(2), pages 327-43. [Downloadable!] (restricted)
  10. Oleg Bondarenko, 2003. "Statistical Arbitrage and Securities Prices," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 16(3), pages 875-919, July. [Downloadable!] (restricted)
  11. Edirisinghe, Chanaka & Naik, Vasanttilak & Uppal, Raman, 1993. "Optimal Replication of Options with Transactions Costs and Trading Restrictions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(01), pages 117-138, March. [Downloadable!]
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