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2003-09-30Buch DOI: 10.18452/8304
On Leland's option hedging strategy with transaction costs
dc.contributor.authorZhao, Yonggan
dc.contributor.authorZiemba, William T.
dc.contributor.editorHigle, Julie L.
dc.contributor.editorRömisch, Werner
dc.contributor.editorSen, Surrajeet
dc.date.accessioned2017-06-16T19:54:46Z
dc.date.available2017-06-16T19:54:46Z
dc.date.created2006-03-01
dc.date.issued2003-09-30none
dc.date.submitted2003-07-27
dc.identifier.urihttp://edoc.hu-berlin.de/18452/8956
dc.description.abstractNonzero transaction costs invalidate the Black-Scholes (1973) arbitrage argument based on continuous trading. Leland (1985) developed a hedging strategy which modifies the Black-Scholes hedging strategy with a volatility adjusted by the length of the rebalance interval and the rate of the proportional transaction cost. Leland claimed that the exact hedge could be achieved in the limit as the length of rebalance intervals approaches zero. Unfortunately, the main theorem (Leland 1985, P1290) is in error. Simulation results also confirm opposite findings to those in Leland (1985). Since standard delta hedging fails to exactly replicate the option in the presence of transaction costs, we study a pricing and hedging model which is similar to the delta hedging strategy with an endogenous parameter, namely the volatility, for the calculation of delta over time. With transaction costs, the optimally adjusted volatility is substantially different from the stock's volatility under the criterion of minimizing the mean absolute replication error weighted by the probabilities that the option is in or out of the money. This model partially explains the phenomenon that the implied volatilities with equity options are skewed. Data on S&P500 index cash options from January to June 2002 are used to illustrate the model. Option prices from our model are highly consistent with the Black-Scholes option prices when transaction costs are zero.eng
dc.language.isoeng
dc.publisherHumboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
dc.relation.ispartofseriesStochastic Programming E-Print Series - 22, SPEPS
dc.subject.ddc510 Mathematik
dc.titleOn Leland's option hedging strategy with transaction costs
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-10059203
dc.identifier.doihttp://dx.doi.org/10.18452/8304
local.edoc.container-titleStochastic Programming E-Print Series
local.edoc.container-titleSPEPS
local.edoc.pages34
local.z-edoc.journal-periodikumAusgabe22,
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-volume2003
local.edoc.container-issue22

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