Option hedging for small investors under liquidity costs
| Autor: | Umut Çetin, Nizar Touzi, H. Mete Soner |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Statistics and Probability
HG Finance 050208 finance jel:D52 Mathematical finance jel:C61 05 social sciences Gamma process jel:G13 01 natural sciences Market liquidity 010104 statistics & probability Bellman equation stochastic target problems differential-equations portfolio constraints viscosity solutions gamma-constraints super-replication pricing theory markets ISI 0502 economics and business 8. Economic growth Arbitrage pricing theory Economics Portfolio QA Mathematics 0101 mathematics Statistics Probability and Uncertainty Viscosity solution Mathematical economics Finance |
| Zdroj: | Finance and Stochastics |
| ISSN: | 1432-1122 0949-2984 |
| DOI: | 10.1007/s00780-009-0116-x |
| Popis: | 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). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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