Leitura do dia - How to Detect an Asset Bubble

How to Detect an Asset Bubble

Robert Jarrow, Younes Kchia, Philip Protter

February 24, 2011

Abstract

After the 2007 credit crisis, nancial bubbles have once again emerged as a topic
of current concern. An open problem is to determine in real time whether or not a
given asset's price process exhibits a bubble. Due to recent progress in the characterization of asset price bubbles using the arbitrage-free martingale pricing technology, we are able to propose a new methodology for answering this question based on the asset's price volatility. We limit ourselves to the special case of a risky asset's price being modeled by a Brownian driven stochastic di fferential equation.
Such models are ubiquitous both in theory and in practice. Our methods use sophisticated volatility estimation techniques combined with the method of reproducing kernel Hilbert spaces.
We illustrate these techniques using several stocks from the alleged internet dot-com
episode of 1998 - 2001, where price bubbles were widely thought to have existed. Our
results support these beliefs.

Um belo artigo propondo técnicas não-paramétricas de detecção de bolhas, usando a teoria de reproducing kernel Hilbert Spaces. Uma única colocação é que o artigo não cita a conexão fundamental entre reproducing kernel Hilbert Spaces e splines e smoothing splines, o que possibilitaria uma técnica estatística de estimação da função de extrapolação.