Option hedging for small investors under liquidity costs
AbstractFollowing 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).
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Bibliographic InfoPaper provided by London School of Economics and Political Science, LSE Library in its series LSE Research Online Documents on Economics with number 28992.
Date of creation: 2010
Date of revision:
Publication status: Published in Finance and Stochastics, 2010, 14(3), pp. 317-341. ISSN: 0949-2984
stochastic target problems; differential-equations; portfolio constraints; viscosity solutions; gamma-constraints; super-replication; pricing theory; markets; ISI;
Find related papers by JEL classification:
- D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Broadie, Mark & Cvitanic, Jaksa & Soner, H Mete, 1998. "Optimal Replication of Contingent Claims under Portfolio Constraints," Review of Financial Studies, Society for Financial Studies, vol. 11(1), pages 59-79.
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- Halil Mete Soner & Guy Barles, 1998. "Option pricing with transaction costs and a nonlinear Black-Scholes equation," Finance and Stochastics, Springer, vol. 2(4), pages 369-397.
- Umut Çetin & Robert Jarrow & Philip Protter, 2004. "Liquidity risk and arbitrage pricing theory," Finance and Stochastics, Springer, vol. 8(3), pages 311-341, 08.
- Peter Bank & Selim G\"okay, 2013. "Superreplication when trading at market indifference prices," Papers 1310.3113, arXiv.org.
- David German & Henry Schellhorn, 2012. "A No-Arbitrage Model of Liquidity in Financial Markets involving Brownian Sheets," Papers 1206.4804, arXiv.org.
- Alexandre Roch, 2011. "Liquidity risk, price impacts and the replication problem," Finance and Stochastics, Springer, vol. 15(3), pages 399-419, September.
- Feyzullah Egriboyun & H. Soner, 2010. "Optimal investment strategies with a reallocation constraint," Computational Statistics, Springer, vol. 71(3), pages 551-585, June.
- Rossella Agliardi & Ramazan Gençay, 2012. "Hedging through a Limit Order Book with Varying Liquidity," Working Paper Series 12_12, The Rimini Centre for Economic Analysis.
- Olivier Gu\'eant & Jiang Pu, 2013. "Option pricing and hedging with execution costs and market impact," Papers 1311.4342, arXiv.org, revised Aug 2014.
- Frédéric Abergel & Grégoire Loeper, 2013. "Pricing and hedging contingent claims with liquidity costs and market impact," Working Papers hal-00802402, HAL.
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