Title: No arbitrage pricing of non-marketed claims in multi-period markets

Authors: Christos E. Kountzakis

Addresses: Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Karlovassi, GR-83 200 Samos, Greece

Abstract: In this paper, we modify the arbitrage-free interval of prices for a non-marketed contingent claim in the finite event-tree model of financial markets, according to the perfect hedging approach being well-known for the two-period model. We prove the existence of solution to the corresponding seller|s and buyer|s price problem for such a claim under no-arbitrage prices for the marketed contracts and we show that each of these problems can be solved by decomposing it into a finite number of one-period linear programming problems solved backwards. Finally, we indicate that the set of the no-arbitrage prices for a non-marketed contingent claim is the interval of the real numbers whose supremum and infimum is the seller|s and the buyer|s price of the claim, respectively. The determination of the set of no-arbitrage prices for a non-marketed contingent claim is related to the utility pricing of such a claim.

Keywords: contingent claims; seller price; buyer price; contingent claim pricing; no-arbitrage pricing; non-marketed claims; multi-period markets; finite event-tree modelling; financial markets; hedging.

DOI: 10.1504/IJFMD.2010.032465

International Journal of Financial Markets and Derivatives, 2010 Vol.1 No.2, pp.125 - 154

Published online: 03 Apr 2010 *

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