Collectively Fluctuating Assets in the Presence of Arbitrage Opportunities and Option Pricing

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 parts 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 Black-Scholes equation for contingent claims is derived, and a connection with the conventional methods of option valuation is indicated.

See also a related paper by A.N.Adamchuk, S.Adamchuk and S.E.Esipov "Arbitrage Relaxation of Instruments with Temporal Constraints"

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JEL Classification: E43, G12, G13, C15