This paper derives an arbitrage-free interest rate movements model (AR model). This model takes the complete term structure as given and derives the subsequent stochastic movement of the term structure such that the movement is arbitrage free. We then show that the AR model can be used to price interest rate contingent claims relative to the observed complete term structure of interest rates. This paper also studies the behavior and the economics of the model. Our approach can be used to price a broad range of interest rate contingent claims, including bond options and callable bonds. INTEREST RATE OPTIONS, CALLABLE bonds, and floating rate notes are a fewexamples of interest rate contingent claims. They are characterized by their finite lives and their price behavior, which crucially depends 'on the term structure and its stochastic movements. In recent years, with the increase in interest rate volatility and the prevalent use of the contingent claims, the pricing of these securities has become a primary concern in financial research. The purpose of this paper is to present a general methodology to price a broad class of interest rate contingent claims.The crux of the problem in pricing interest rate contingent claims is to model the term structure movements and to relate the movements to the assets' prices.Much academic literature has been devoted to this problem. One earlier attempt is that of Pye [15]. He assumed that the interest rates move according to a (Markov) transition probabilities matrix, and he then used the expectation hypothesis to price the expected cash flow of the asset-in his case, a callable bond (Pye [16]). Recently, investigators have focused more on developing equilibrium models.Cox, Ingersoll, and Ross (CIR) [7] assumed that the short rate follows a meanreverting process. By further assuming that all interest rate contingent claims are priced contingent on only the short rate, using a continuous arbitrage argument they derived an equilibrium pricing model. Brennan and Schwartz (BS) [2] extended the CIR model to incorporate both short and long rates and studied the pricing of a broad range of contingent claims (BS [1, 3]). In these for their helpful comments on the earlier version of the paper. We would also like to thank, in particular, the referee, Eduardo Schwartz, for many of his helpful comments on this paper. We are responsible for the remaining errors. 1011 1012The Journal of Finance approaches, both the term structure and the contingent claims are derived in an equilibrium context.1 This paper proposes an alternative approach to these pricing models. We take the term structure as given and derive the feasible subsequent term structure movements. These movements must satisfy certain constraints to ensure that they are consistent with an equilibrium framework. Specifically, the movements cannot permit arbitrage profit opportunities. We shall call these interest rate movements arbitrage-free rate movements (AR). When the AR movements are determined, the interest rate contingent cl...

The behavior of competing dealers in securities markets is analyzed. Securities are characterized by stochastic returns and stochastic transactions. Reservation bid and ask prices of dealers are derived under alternative assumptions about the degree to which transactions are correlated across stocks at a given time and over time in a given stock. The conditions for interdealer trading are specified, and the equilibrium distribution of dealer inventories and the equilibrium market spread are derived. Implications for the structure of securities markets are examined. IN THIS PAPER the behavior of competing dealers in security marketsis examined. Much of the theoretical work on dealers (Demsetz [6], Tinic [18], Garman [8], Stoll [16], Amihud and Mendelson [1], Ho and Stoll [11], Copeland and Galai [3], Mildenstein and Schleef [13]) has recognized that dealers may face competition from other dealers or investors placing limit orders, but nonetheless has analyzed only a single (representative) dealer. This approach is quite reasonable for the New York Stock Exchange specialist who has a quasi-monopoly position, but it is less applicable when considering other markets such as the over-thecounter market where there are several dealers with equal access to the market. Similarly the empirical studies of dealer bid-ask spreads (Demsetz [6], Tinic [18], Tinic and West [19], Benston and Hagerman [2], Stoll [17], Smidt [15]) have either been based on models of a single dealer or have lacked a theoretical foundation based on the microeconomics of the dealer. This paper develops a theoretical model of equilibrium in a market with competing dealers and provides a basis for empirical work that would distinguish competing and monopolistic dealer markets. The paper is concerned with the behavior and interaction of individual competing dealers and with the determination of the market bid-ask spread. Markets with several dealers, several stocks and several periods are considered. Dealers bear risk arising not only from uncertainty about the returns on their inventories but also from uncertainty about the arrival of transactions. Each dealer also recognizes that his welfare depends on the actions of other dealers and each sets bid and ask prices to maximize his own expected utility of terminal wealth. A recent paper by Cohen, Maier, Schwartz and Whitcomb [5] examines similar issues in the context of an auction market in which the market spread is determined by limit orders. However, unlike the model of this paper, their analysis is not based as clearly on a model of individual traders' maximizing behaviors nor are the costs of placing * Financial support of the Dean's Fund for Faculty Research at the Owen Graduate School of Management is gratefully acknowledged. 1053 1054 The Journal of Finance 1 The formal model is changed slightly in that we use discrete time stochastic processes in this paper rather than the continuous time stochastic processes in Ho and Stoll [11]. Some preliminary results under competition-particularly the idea o...

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