Arbitrage in securities markets with short-sales constraints

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Arbitrage in securities markets with short-sales constraints

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Title: Arbitrage in securities markets with short-sales constraints
Author: Jouini, Elyès; Kallal, Hedi
Type: Article accepté pour publication ou publié
Date de création: 07-1995
Résumé en anglais: In this paper we derive the implications of the absence of arbitrage in securities markets models where traded securities are subject to short-sales constraints and where the borrowing and lending rates differ. We show that a securities price system is arbitrage free if and only if there exists a numeraire and an equivalent probability measure for which the normalized (by the numeraire) price processes of traded securities are supermartingales. Also, the tightest arbitrage bounds that can be inferred on the price of a contingent claim without knowing agents’preferences are equal to its largest and smallest expected normalized payoff with respect to the supermartingale measures. In the case where the underlying security price follows a diffusion process and where short selling is possible but costly, we derive partial differential equations that must be satisfied by the arbitrage bounds on derivative securities prices, and we determine optimal hedging strategies. We compute the arbitrage bounds on common securities numerically for several values of the borrowing and short-selling costs and show that they can be quite sharp.
Indexation documentaire: Economie financière
Sujet(s): Short-sales constraints; borrowing costs; martingale approach; equivalent supermatingale and submartingale measures; perturbed heat equation; arbitrage bounds; hedging
JEL Code: G10; G13; C73
URL de la notice: http://basepub.dauphine.fr/xmlui/handle/123456789/5647
PUBLIE DANS
Nom de la revue: Mathematical Finance
Volume: 5
Numéro: 3
Parution: 07-1995
Pages: 197-232
Editeur: Wiley
Réf. Version publiée: http://dx.doi.org/10.1111/j.1467-9965.1995.tb00065.x

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