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Options hedging under liquidity costs

Çetin, Umut and Soner, Halil Mete and Touzi, Nizar (2007) Options hedging under liquidity costs. [Working Paper / Technical Report] Sabanci University ID:SU_FMAN_2007/0017

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Abstract

Following the framework of Cetin, Jarrow and Protter (CJP) we study the problem of super-replication in presence of liquidity costs under additional restrictions on the gamma of the hedging strategies in a generalized Black-Scholes economy. We find that the minimal super-replication price is different than the one suggested by the Black-Scholes formula and is the unique viscosity solution of the associated dynamic programming equation. This is in contrast with the results of CJP who find that the arbitrage free price of a contingent claim coincides with the Black-Scholes price. However, in CJP a larger class of admissible portfolio processes is used and the replication is achieved in the L^2 approximating sense.

Item Type:Working Paper / Technical Report
Uncontrolled Keywords:Super-replication, liquidity cost, Gamma process, parabolic majorant, double stochastic integrals.
Subjects:H Social Sciences > HG Finance
Q Science > QA Mathematics
ID Code:7103
Deposited By:Halil Mete Soner
Deposited On:19 Nov 2007 12:22
Last Modified:11 Sep 2008 15:28

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