Consider the postage stamp. As title to a future good (or, in this case, service) with monetary value, this humble object is essentially the same as a security. Its value, 37 cents, can be identiÞed with the present value of the service (delivery of a letter) to which its owner is entitled.

This article documents an apparentpricing anomaly

A recursive test procedure is suggested that provides a mechanism for testing explosive behavior, date-stamping the origination and collapse of economic exuberance, and providing valid confidence intervals for explosive growth rates. The method involves the recursive implementation of a right-side unit root test and a sup test, both of which are easy to use in practical applications, and some new limit theory for mildly explosive processes. The test procedure is shown to have discriminatory power in detecting periodically collapsing bubbles, thereby overcoming a weakness in earlier applications of unit root tests for economic bubbles. An empirical application to Nasdaq stock price index in the 1990s provides confirmation of explosiveness and date-stamps the origination of financial exuberance to mid-1995, prior to the famous remark in December 1996 by Alan Greenspan about irrational exuberance in financial

This paper demonstrates that an asset pricing model with least-squares learning can lead to bubbles and crashes as endogenous responses to the fundamentals driving asset prices. When agents are risk-averse they generate forecasts of the conditional variance of a stock’s return. Recursive updating of the conditional variance and expected return implies two mechanisms through which learning impacts stock prices: occasional shocks may lead agents to lower their risk estimate and increase their expected return, thereby triggering a bubble; along a bubble path recursive estimates of risk will increase and crash the bubble. JEL Classifications: G12; G14; D82; D83 Key Words: Risk, asset pricing, bubbles, adaptive learning. Thus, this vast increase in the market value of asset claims is in part the indirect result of investors accepting lower compensation for risk. Such an increase in market value is too often viewed by market participants as structural and permanent... Any onset of increased investor caution elevates risk premiums and, as a consequence, lowers asset values and promotes the liquidation of the debt that supported higher asset prices. This is the reason that history has not dealt kindly with the aftermath of protracted periods of low risk premiums.

This paper studies asset price bubbles in a continuous time model using the local martingale framework. Providing careful definitions of the asset’s market and fundamental price, we characterize all possible price bubbles in an incomplete market satisfying the ”no free lunch with vanishing risk” and ”no dominance” assumptions. We propose a new theory for bubble birth which involves a nontrivial modification of the classical framework. We show that the two leading models for bubbles as either charges or as strict local martingales, respectively, are equivalent. Finally, we investigate the pricing of derivative securities in the presence of asset price bubbles, and we show that: (i) European put options can have no bubbles, (ii) European call options and discounted forward prices can have bubbles, but the magnitude of their bubbles must equal the magnitude of the asset’s price bubble, (iii) with no dividends, American call prices must always equal an otherwise identical European call’s price, regardless of bubbles, (iv) European put-call parity in market prices must always hold, regardless of bubbles, and (v) futures price bubbles can exist and they are independent of bubbles in the underlying asset’s price. These results imply that in a market satisfying NFLVR and no dominance, in the presence of an asset price bubble, risk neutral valuation can not be used to match call option prices. We propose, but do not implement, some new tests for the existence of asset price bubbles using derivative securities.

We estimate a dynamic asset pricing model characterized by heterogeneous boundedly rational agents. The fundamental value of the risky asset is publicly available to all agents, but they have different beliefs about the persistence of deviations of stock prices from the fundamental benchmark. An evolutionary selection mechanism based on relative past profits governs the dynamics of the fractions and switching of agents between different beliefs or forecasting strategies. A strategy attracts more agents if it performed relatively well in the recent past compared to other strategies. We estimate the model to annual US stock price data from 1871 until 2003. The estimation results support the existence of two expectation regimes, and a bootstrap F-test rejects linearity in favor of our nonlinear two-type heterogeneous agent model. One regime can be characterized as a fundamentalists regime, because agents believe in mean reversion of stock prices toward the benchmark fundamental value. The second regime can be characterized as a chartist, trend following regime because agents expect the deviations from the fundamental to trend. The fractions of agents using the fundamentalists and trend following forecasting rules show substantial time variation and switching between predictors. The model offers an explanation for the recent stock prices run-up. Before the 90s the trend following regime was active only occasionally. However, in the late 90s the trend following regime persisted and created an extraordinary deviation of stock prices from the fundamentals. Recently, the activation of the mean reversion regime has contributed to drive stock prices back closer to their fundamental valuation.

Error correction models are widely used to estimate dynamic cointegrated systems. In most applications, estimated error correction models are reduced form models. As a result, nonstructural speed of adjustment coefficients are estimated in these applications. A single equation instrumental variable method can be used to estimate a structural speed of adjustment coefficient. This paper develops a system instrumental variable method to estimate the structural speed of adjustment coefficient in an error correction model. This method utilizes Hansen and Sargent’s (1982) instrumental variable estimator for linear rational expectations models, and is applied to an exchange rate model with sticky prices.

A model for a financial asset is constructed with two types of agents, who differ in terms of their beliefs. The proportion of the two types changes over time according to stochastic processes which model the interaction between the agents. Agents do not persist in holding “wrong ” beliefs and bubble–like phenomena in the asset price occur. We consider tests for detecting bubbles in the conditional mean and multiple changes in the conditional variance of the process. A wavelet analysis of the series generated by our models shows that the strong persistence in the volatility is likely to be the outcome of a mix of changes in regimes and a moderate level of long–range dependence. These results are consistent with what has been observed by Kokoszka and Teyssière (2002) and Teyssière (2003).

this paper, we detect whether the recent experience of the

A number of papers claim that a Log Periodic Power Law (LPPL) fitted to financial market bubbles that precede large market falls or ‘crashes’, contain parameters that are confined within certain ranges. The mechanism that has been claimed as underlying the LPPL, is based on influence percolation and a martingale condition. This paper examines these claims and the robustness of the LPPL for capturing large falls in the Hang Seng stock market index, over a 30-year period, including the current global downturn. We identify 11 crashes on the Hang Seng market over the period 1970 to 2008. The fitted LPPLs have parameter values within the ranges specified post hoc by Johansen and Sornette [12] for only seven of these crashes. Interestingly, the LPPL fit could have predicted the substantial fall in the Hang Seng index during the recent global downturn. We also find that influence percolation combined with a martingale condition holds for only half of the pre-crash bubbles previously reported. Overall, the mechanism posited as underlying the LPPL does not do so, and the data used to support the fit of the LPPL to bubbles does so only partially. 1