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This article is cited in 8 scientific papers (total in 8 papers)
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Collectively fluctuating assets in the presence of arbitrage opportunities, and option pricing
A. N. Adamchuka, S. E. Esipovb a Department of Physics, Syracuse
University
b Department of Physics and James Frank Institute, University of Chicago
Abstract:
Methods of functional analysis are applied to describe collectively fluctuating default-free pure discount bonds subject to trading-related noise which generates arbitrage opportunities. Two key elements of the model are: (i) the naturally incorporated fixed bond price at maturity which is achieved by making use of only those fluctuating paths of price motion which terminate at a specified final condition, and (ii) the most attractive arbitrage opportunities between bonds with close maturities, with modeled a local linear approximation. The model can be written in different closed forms as a stochastic partial differential equation. The functional Black—Scholes equation for contingent claims is derived, and a connection with the conventional methods of option valuation is indicated.
Received: November 1, 1997
Citation:
A. N. Adamchuk, S. E. Esipov, “Collectively fluctuating assets in the presence of arbitrage opportunities, and option pricing”, UFN, 167:12 (1997), 1295–1306; Phys. Usp., 40:12 (1997), 1239–1248
Linking options:
https://www.mathnet.ru/eng/ufn1398 https://www.mathnet.ru/eng/ufn/v167/i12/p1295
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Abstract page: | 166 | Full-text PDF : | 56 | First page: | 1 |
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