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Type: Journal article
Title: Arbitrage in a discrete version of the Wick-Fractional Black Scholes model
Author: Bender, C.
Elliott, R.
Citation: Mathematics of Operations Research, 2004; 29(4):935-945
Publisher: Inst Operations Research Management Sciences
Issue Date: 2004
ISSN: 0364-765X
Statement of
Christian Bender and Robert J. Elliott
Abstract: We consider binary market models based on the discrete Wick product instead of the pathwise product and provide a sufficient criterion for the existence of an arbitrage. This arbitrage is explicitly constructed in the class of self-financing one-step buy-and-hold strategies, (i.e., the investor holds shares of the stock only at one time step). Using coefficients obtained from an approximation of a fractional Brownian motion with Hurst parameter ½ < H < 1 the result is applied to a discrete version of the (Wick-)fractional Black-Scholes market.
Keywords: Arbitrage
binary market models
discrete Wick products
fractional Brownian motion
DOI: 10.1287/moor.1040.0096
Published version:
Appears in Collections:Applied Mathematics publications
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