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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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 |
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| Official URL: | http://www.springerlink.com/content/0949-2984 |
| Additional Information: | © 2010 Springer-Verlag, Part of Springer Science+Business Media |
| Uncontrolled Keywords: | stochastic target problems, differential-equations, portfolio constraints, viscosity solutions, gamma-constraints, super-replication, pricing theory, markets, ISI |
| 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 |
| Rights: | http://www.lse.ac.uk/library/rights/LSERO.htm |
| Identification Number: | UT ISI:000280076300001 |
| URL: | http://eprints.lse.ac.uk/28992/ |
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