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Modelling Bond Markets

Philippe Moutot, Imma Curato, and Rafaela Guberowic

Abstract

The concept of market freeze and the notion of excessive bid/ask spreads have long been at odds with the Walras Law. As a consequence, only a limited literature deals with their cases and identifies their causes, usually concentrating on imperfect information and adverse selection, self-fulfilling prophecies and herding behaviours. Moreover, as the associated price movements often reach amplitudes difficult to generate in general equilibrium models, they are increasingly explained by reference to the notion of uncertainty.

Nevertheless, such freezes and excessive spreads do happen and recently did in major markets, making their circumstances and modelling worth exploring. Also, the imperfectness of information does not constitute a very likely explanation of the sovereign bond crisis nor of recent market incidents. Moreover, this fails to explain why traditionally deep markets may see their turnover plummet in periods of financial uncertainty but in the absence of abrupt changes to their relevant fundamentals.

This paper follows another modelling strategy. It assumes that the medium term structure of bond markets is given, with a few market-makers competitively determining spreads, in line with recent literature on intermediation. However, markets are assumed to function on a periodic rather than continuous basis and their participants, who form rational expectations, are submitted to end-of-period financial constraints. The paper therefore gives special importance to the way payments are decided and reflects the cost of securities issuance and trading, a usually small and neglected component of the bond price in normal times. This is in line with the logic of Rosenthal and Wang (1993) for whom budget constraints and trading costs were leading to market freezes.

This strategy is helpful. First, the model which is formulated in discrete time with an infinite horizon, can be solved, at least numerically. Moreover, solutions for constant discount rates of utility allow calculating solutions for cases where discount rates of utility follow random walks.

Second, the model generates a dynamics of the bid-ask spread which varies across situations. In normal times, or for usual discount rates, spreads are small. By contrast, spreads grow exponentially for low discount rates. Moreover, the model mimics the decrease in turnover and the related increase of spreads observed in uncertain times. Finally, the solutions of the model are non-existent when the discount rate of utility is too low. Hence equilibria which would exist with cash-in-advance constraints do not with cash-at-the-end-of-period constraints. As a result, traditional economic fundamentals are not necessarily the only source of the large increase in spreads and lower turnover sometimes apparent on sovereign bond markets.

Third, changes in market structure have clear impacts on spreads and market turnover. This has policy consequences.

Fourth, we assume that the discount rates of utility of traders in three different markets follow correlated random walks. The evolution of spreads may evoke features of spreads within the euro area during the sovereign bond crisis.

Keywords: market freeze, payments, financial uncertainty