Eccessiva sicurezza, speculazione e bolle finanziarie

Financial bubbles occur whenever the price of an asset is different from the present value of the stream of expected dividends. Bubbles are generally characterized by a dramatic increase in the price of some assets followed by an unexpected crash. Historicaly, we observed several famous examples: among others, we recall the Dutch Tulip Mania (1634-37), the Mississippi Bubble (1719-20) and the South Sea Bubble (1720). In fi- nance, bubbles have been studied according to two different approaches: the former refers to the so-called rational bubbles, while the latter sees in the heterogeneity of beliefs the main cause of the existence of bubbles. The main feature of the rationality approach is the assumption of rational expectation and rational behaviour of agents. Even under these conditions, there may still be deviations of the price from its value, as showed by Blanchard and Watson [1982]. Similarly, Santos and Woodford [1997] de- mostrated that bubbles could exist in equilibrium. The infinite horizon and asymmetric information assumptions must be made as well. In fact Tirole [1982] argued that in a discrete-time finite-horizon setting with symmetric information stock prices cannot deviate from fundamentals if traders are rational. On the contrary, heterogeneous beliefs may arise when traders have different prior distributions, which could be possibly due to psychological bias: for example, heterogeneity in beliefs may occur when people overestimate the information they have, as discussed in this paper; this is the definition of overconfidence. Differently from the case of asymmetric information, individuals may share their information but they agree to disagree because of their non-common priors; so they cannot use price to obtain new information. Generally, the short-sale contraint is also added to the model, so as to avoid the compensating effect of the pessimists who can sell an infinite quantity of assets. This results in an overpriced asset, which is the bubble. Scheinkman and Xiong [2003] were the first to take into account the speculative motive. The model presented below is based on that paper. There is a single risky asset and two risk-neutral agents in an infinite-horizon setting. The information is available to both agents which update their information continuously. Each individual overestimates her signal and this generates heterogeneity in beliefs. Moreover, at each instant the holder of the asset has the option to sell it; clearly the value of this American option affects the price of the asset. The resale option value, which is exactly the difference between the price of the asset and its fundamental, is the bubble. It will be shown that trade occurs whenever the difference in beliefs is sufficiently high and that this difference is strictly related to transaction costs; when there are no transaction costs, the trade is immediate. Furthermore, there is an extra price volatility component due to overconfidence of agents. Finally, we allow agents to have different levels of overconfidence and we ask ourselves what happens as these levels change over time. In particular we focus on the effect of an absolute increase or decrease in the difference of the overconfidence parameters, no matter which agent is holding the asset at a specific instant, and derive the corresponing variations in i) the resale option value, ii) the price and the volatility of the asset and iii) the average duration between trades.