Option hedging for small investors under liquidity costs

Soner, H. Mete, Cetin, Umut ORCID: 0000-0001-8905-853X and Touzi, Nizar (2010) Option hedging for small investors under liquidity costs. Finance and Stochastics, 14 (3). pp. 317-341. ISSN 0949-2984

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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).

Item Type:	Article
Official URL:	http://www.springerlink.com/content/0949-2984
Additional Information:	© 2010 Springer-Verlag, Part of Springer Science+Business Media
Divisions:	LSE
Subjects:	H Social Sciences > HG Finance Q Science > QA Mathematics
JEL classification:	D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D52 - Incomplete Markets G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing; Futures Pricing C - Mathematical and Quantitative Methods > C6 - Mathematical Methods and Programming > C61 - Optimization Techniques; Programming Models; Dynamic Analysis
Date Deposited:	27 Aug 2010 10:48
Last Modified:	11 Dec 2024 23:41
Funders:	Societe Generale, Federation Bancaire Francaise, EDF, Calyon, European Science Foundation
URI:	http://eprints.lse.ac.uk/id/eprint/28992

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