Option hedging for small investors under liquidity costs

Following the framework of C¸etin, Jarrow and Protter [4] we study the problem of super-replication in 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 [4] who find that the arbitrage free price of a contingent claim coincides with the Black-Scholes price. However, in [4] a larger class of admissible portfolio processes is used and the replication is achieved in the L2 approximating sense. Keywords Super-replicatio · liquidity cost · Gamma process · parabolic majorant · PDE valuation PACS 91B28 · 35K55 · 60H30

• Type: Journal
• Year: 2010
• Where: FS
• Authors: Umut Çetin, H. Mete Soner, Nizar Touzi
• Keywords: Black-Scholes, FS 2010, Generalized Black-scholes Economy, Minimal Super-replication Price