Collectively fluctuating assets in the presence of arbitrage opportunities, and option pricing

A.N. Adamchuk^a, S.E. Esipov^b
^aThe University of Chicago, 5801 South Ellis Ave., Chicago, Illinois, 60637, USA
^bDepartment of Physics and James Frank Institute, University of Chicago, Chicago, Illinois, USA

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.

PACS: 01.75.+m, 02.30.Sa, 02.90.+p, 89.90.+n (all)
DOI: 10.1070/PU1997v040n12ABEH000319
URL: https://ufn.ru/en/articles/1997/12/b/
Web of Science

000071721900002
Citation: Adamchuk A N, Esipov S E "Collectively fluctuating assets in the presence of arbitrage opportunities, and option pricing" Phys. Usp. 40 1239–1248 (1997)

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Оригинал: Адамчук А Н, Есипов С Е «Коллективно флуктуирующие активы при наличии арбитражных возможностей и оценка платежных обязательств» УФН 167 1295–1306 (1997); DOI: 10.3367/UFNr.0167.199712b.1295

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