Arbitrage in securities markets with short-sales constraints
AbstractIn 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.
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Bibliographic InfoPaper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/5647.
Date of creation: Jul 1995
Date of revision:
Publication status: Published in Mathematical Finance, 1995, Vol. 5, no. 3. pp. 197-232.Length: 35 pages
Short-sales constraints; borrowing costs; martingale approach; equivalent supermatingale and submartingale measures; perturbed heat equation; arbitrage bounds; hedging;
Find related papers by JEL classification:
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
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