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Option hedging for small investors under liquidity costs

Soner, H. Mete, Cetin, Umut 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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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:
Additional Information: © 2010 Springer-Verlag, Part of Springer Science+Business Media
Library of Congress subject classification: H Social Sciences > HG Finance
Q Science > QA Mathematics
Journal of Economic Literature Classification System: 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
Funders: Societe Generale, Federation Bancaire Francaise, EDF, Calyon, European Science Foundation
Date Deposited: 27 Aug 2010 10:48

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