Option hedging for small investors under liquidity costs

Umut Çetin, H. Mete Soner, Nizar Touzi

Research output: Contribution to journalArticle

52 Scopus citations

Abstract

Following the framework of Çetin 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 Çetin 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 Çetin et al. (Finance Stoch. 8:311-341, 2004) a larger class of admissible portfolio processes is used, and the replication is achieved in the L2 approximating sense.

Original languageEnglish (US)
Pages (from-to)317-341
Number of pages25
JournalFinance and Stochastics
Volume14
Issue number3
DOIs
StatePublished - Jan 1 2010
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Finance
  • Statistics, Probability and Uncertainty

Keywords

  • Gamma process
  • Liquidity cost
  • PDE valuation
  • Parabolic majorant
  • Super-replication

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