Insolvency Traps and Multiple Equilibria Complex Dynamics in a Simple Bond Market

The recent nancial market turmoil has raised the question whether certain countries, in particular Italy and Spain, were facing a liquidity or a solvency problem. Some economists re{phrased this problem, by asking whether those countries' crisis was triggered by investors' self- ful lling expectations which are not, or not entirely, justi ed by fundamentals. In the academic literature and the specialized press, this phenomenon is characterized by two related, "perverse" features: the presence of upward-sloping tracts of the demand for bond function and the associated multiple equilibria. In this paper, we discuss the question by means of a simpli ed mathematical representation of a single sovereign bond market, and show that the dynamics of the bond price (equivalently its yield) may be greatly more complicated than we are often led to believe. Even in the most favorable circumstances { a single equilibrium and an everywhere downward{sloping excess{demand function { the equilibrium may not be stable and the state variables may converge to a cycle around it, and more or less far from it. Second, if the single equilibrium is unstable and, due to the presence of upward{sloping tracts of the demand curve, the controlling map is non-monotonic, the asymptotic dynamics of the bond's price (and the corresponding yield) may be very complicated. In the multiple equilibria case, many different, more or less complicated dynamics (cyclical with different periods or even chaotic) may occur. These results suggest that the task of a central bank trying to stabilize the sovereign bond market by means of an external intervention may turn out to be far more dicult than expected.