Option hedging for small investors under liquidity costs

H. Mete Soner, Umut Cetin and Nizar Touzi

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: Following the framework of Cetin et al. (finance stoch. 8:311-341, 2004), we study the problem of super-replication in the 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 from 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 Cetin et al. (Finance Stoch. 8:311-341, 2004), who find that the arbitrage-free price of a contingent claim coincides with the Black-Scholes price. However, in Cetin et al. (Finance Stoch. 8:311-341, 2004) a larger class of admissible portfolio processes is used, and the replication is achieved in the L (2) approximating sense. JEL (C61 - G13 - D52).

Keywords: stochastic target problems; differential-equations; portfolio constraints; viscosity solutions; gamma-constraints; super-replication; pricing theory; markets; ISI (search for similar items in EconPapers)
JEL-codes: C61 D52 G13 (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (38)

Published in Finance and Stochastics, 2010, 14(3), pp. 317-341. ISSN: 0949-2984

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