We analyze a controlled price formation experiment in the laboratory that
shows evidence for bubbles. We calibrate two models that demonstrate with high
statistical significance that these laboratory bubbles have a tendency to grow
faster than exponential due to positive feedback. We show that the positive
feedback operates by traders continuously upgrading their over-optimistic
expectations of future returns based on past prices rather than on realized
returns.

On December 16th, 2011, Zynga, the well-known social game developing company
went public. This event followed other recent IPOs in the world of social
networking companies, such as Groupon or Linkedin among others. With a
valuation close to 7 billion USD at the time when it went public, Zynga became
one of the biggest web IPOs since Google. This recent enthusiasm for social
networking companies raises the question whether they are overvalued.

We present a novel methodology to determine the fundamental value of firms in
the social-networking sector, motivated by recent realized IPOs and by reports
that suggest sky-high valuations of firms such as facebook, Groupon, LinkedIn
Corp., Pandora Media Inc, Twitter, Zynga.

Financial markets are well known for their dramatic dynamics and consequences
that affect much of the world's population. Consequently, much research has
aimed at understanding, identifying and forecasting crashes and rebounds in
financial markets. The Johansen-Ledoit-Sornette (JLS) model provides an
operational framework to understand and diagnose financial bubbles from
rational expectations and was recently extended to negative bubbles and
rebounds.

We present an extension of the Johansen-Ledoit-Sornette (JLS) model to
include an additional pricing factor called the "Zipf factor", which describes
the diversification risk of the stock market portfolio. Keeping all the
dynamical characteristics of a bubble described in the JLS model, the new model
provides additional information about the concentration of stock gains over
time. This allows us to understand better the risk diversification and to
explain the investors' behavior during the bubble generation.

Using a recently introduced method to quantify the time varying lead-lag
dependencies between pairs of economic time series (the thermal optimal path
method), we test two fundamental tenets of the theory of fixed income: (i) the
stock market variations and the yield changes should be anti-correlated; (ii)
the change in central bank rates, as a proxy of the monetary policy of the
central bank, should be a predictor of the future stock market direction.

This is the third installment of the Financial Bubble Experiment. Here we
provide the digital fingerprint of an electronic document in which we identify
27 bubbles in 27 different global assets; for 25 of these assets, we present
windows of dates of the most likely ending time of each bubble. We will provide
that document of the original analysis on 2 May 2011.

Leverage is strongly related to liquidity in a market and lack of liquidity
is considered a cause and/or consequence of the recent financial crisis. A
repurchase agreement is a financial instrument where a security is sold
simultaneously with an agreement to buy it back at a later date. Repurchase
agreements (repos) market size is a very important element in calculating the
overall leverage in a financial market. Therefore, studying the behavior of
repos market size can help to understand a process that can contribute to the
birth of a financial crisis.

We introduce the concept of "negative bubbles" as the mirror image of
standard financial bubbles, in which positive feedback mechanisms may lead to
transient accelerating price falls. To model these negative bubbles, we adapt
the Johansen-Ledoit-Sornette (JLS) model of rational expectation bubbles with a
hazard rate describing the collective buying pressure of noise traders.

By combining (i) the economic theory of rational expectation bubbles, (ii)
behavioral finance on imitation and herding of investors and traders and (iii)
the mathematical and statistical physics of bifurcations and phase transitions,
the log-periodic power law (LPPL) model has been developed as a flexible tool
to detect bubbles. The LPPL model considers the faster-than-exponential (power
law with finite-time singularity) increase in asset prices decorated by
accelerating oscillations as the main diagnostic of bubbles.

We propose two rational expectation models of transient financial bubbles
with heterogeneous arbitrageurs and positive feedbacks leading to
self-reinforcing transient stochastic faster-than-exponential price dynamics.
As a result of the nonlinear feedbacks, the termination of a bubble is found to
be characterized by a finite-time singularity in the bubble price formation
process ending at some potential critical time $\tilde{t}_c$, which follows a
mean-reversing stationary dynamics.