Mathematically detecting stock market bubbles before they burst

ScienceDaily (Oct. 31, 2011) — From the dotcom bust in the late nineties to the housing crash in the run-up to the 2008 crisis, financial bubbles have been a topic of major concern. Identifying bubbles is important in order to prevent collapses that can severely impact nations and economies.

A paper published this month in the SIAM Journal on Financial Mathematics addresses just this issue. Opening fittingly with a quote from New York Federal Reserve President William Dudley emphasizing the importance of developing tools to identify and address bubbles in real time, authors Robert Jarrow, Younes Kchia, and Philip Protter propose a mathematical model to detect financial bubbles.

A financial bubble occurs when prices for assets, such as stocks, rise far above their actual value. Such an economic cycle is usually characterized by rapid expansion followed by a contraction, or sharp decline in prices.

"It has been hard not to notice that financial bubbles play an important role in our economy, and speculation as to whether a given risky asset is undergoing bubble pricing has approached the level of an armchair sport. But bubbles can have real and often negative consequences," explains Protter, who has spent many years studying and analyzing financial markets.

"The ability to tell when an asset is or is not in a bubble could have important ramifications in the regulation of the capital reserves of banks as well as for individual investors and retirement funds holding assets for the long term. For banks, if their capital reserve holdings include large investments with unrealistic values due to bubbles, a shock to the bank could occur when the bubbles burst, potentially causing a run on the bank, as infamously happened with Lehman Brothers, and is currently happening with Dexia, a major European bank," he goes on to explain, citing the significance of such inflated prices.

Using sophisticated mathematical methods, Protter and his co-authors answer the question of whether the price increase of a particular asset represents a bubble in real time. "[In this paper] we show that by using tick data and some statistical techniques, one is able to tell with a large degree of certainty, whether or not a given financial asset (or group of assets) is undergoing bubble pricing," says Protter.

This question is answered by estimating an asset's price volatility, which is stochastic or randomly determined. The authors define an asset's price process in terms of a standard stochastic differential equation, which is driven by Brownian motion. Brownian motion, based on a natural process involving the erratic, random movement of small particles suspended in gas or liquid, has been widely used in mathematical finance. The concept is specifically used to model instances where previous change in the value of a variable is unrelated to past changes.

The key characteristic in determining a bubble is the volatility of an asset's price, which, in the case of bubbles is very high. The authors estimate the volatility by applying state of the art estimators to real-time tick price data for a given stock. They then obtain the best possible extension of this data for large values using a technique called Reproducing Kernel Hilbert Spaces (RKHS), which is a widely used method for statistical learning.

"First, one uses tick price data to estimate the volatility of the asset in question for various levels of the asset's price," Protter explains. "Then, a special technique (RKHS with an optimization addition) is employed to extrapolate this estimated volatility function to large values for the asset's price, where this information is not (and cannot be) available from tick data. Using this extrapolation, one can check the rate of increase of the volatility function as the asset price gets arbitrarily large. Whether or not there is a bubble depends on how fast this increase occurs (its asymptotic rate of increase)."

If it does not increase fast enough, there is no bubble within the model's framework.

The authors test their methodology by applying the model to several stocks from the dot-com bubble of the nineties. They find fairly successful rates in their predictions, with higher accuracies in cases where market volatilities can be modeled more efficiently. This helps establish the strengths and weaknesses of the method.

The authors have also used the model to test more recent price increases to detect bubbles. "We have found, for example, that the IPO [initial public offering] of LinkedIn underwent bubble pricing at its debut, and that the recent rise in gold prices was not a bubble, according to our models," Protter says.

It is encouraging to see that mathematical analysis can play a role in the diagnosis and detection of bubbles, which have significantly impacted economic upheavals in the past few decades.

Robert Jarrow is a professor at the Johnson Graduate School of Management at Cornell University in Ithaca, NY, and managing director of the Kamakura Corporation. Younes Kchia is a graduate student at Ecole Polytechnique in Paris, and Philip Protter is a professor in the Statistics Department at Columbia University in New York.

Professor Protter's work was supported in part by NSF grant DMS-0906995.

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Journal Reference:

Robert Jarrow, Younes Kchia, and Philip Protter. How to Detect an Asset Bubble. SIAM J. Finan. Math., 2011; 2, pp. 839-865 [link]

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Disclaimer: Views expressed in this article do not necessarily reflect those of ScienceDaily or its staff.

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Mathematically detecting stock market bubbles before they burst

ScienceDaily (Oct. 31, 2011) — From the dotcom bust in the late nineties to the housing crash in the run-up to the 2008 crisis, financial bubbles have been a topic of major concern. Identifying bubbles is important in order to prevent collapses that can severely impact nations and economies.

A paper published this month in the SIAM Journal on Financial Mathematics addresses just this issue. Opening fittingly with a quote from New York Federal Reserve President William Dudley emphasizing the importance of developing tools to identify and address bubbles in real time, authors Robert Jarrow, Younes Kchia, and Philip Protter propose a mathematical model to detect financial bubbles.

A financial bubble occurs when prices for assets, such as stocks, rise far above their actual value. Such an economic cycle is usually characterized by rapid expansion followed by a contraction, or sharp decline in prices.

"It has been hard not to notice that financial bubbles play an important role in our economy, and speculation as to whether a given risky asset is undergoing bubble pricing has approached the level of an armchair sport. But bubbles can have real and often negative consequences," explains Protter, who has spent many years studying and analyzing financial markets.

"The ability to tell when an asset is or is not in a bubble could have important ramifications in the regulation of the capital reserves of banks as well as for individual investors and retirement funds holding assets for the long term. For banks, if their capital reserve holdings include large investments with unrealistic values due to bubbles, a shock to the bank could occur when the bubbles burst, potentially causing a run on the bank, as infamously happened with Lehman Brothers, and is currently happening with Dexia, a major European bank," he goes on to explain, citing the significance of such inflated prices.

Using sophisticated mathematical methods, Protter and his co-authors answer the question of whether the price increase of a particular asset represents a bubble in real time. "[In this paper] we show that by using tick data and some statistical techniques, one is able to tell with a large degree of certainty, whether or not a given financial asset (or group of assets) is undergoing bubble pricing," says Protter.

This question is answered by estimating an asset's price volatility, which is stochastic or randomly determined. The authors define an asset's price process in terms of a standard stochastic differential equation, which is driven by Brownian motion. Brownian motion, based on a natural process involving the erratic, random movement of small particles suspended in gas or liquid, has been widely used in mathematical finance. The concept is specifically used to model instances where previous change in the value of a variable is unrelated to past changes.

The key characteristic in determining a bubble is the volatility of an asset's price, which, in the case of bubbles is very high. The authors estimate the volatility by applying state of the art estimators to real-time tick price data for a given stock. They then obtain the best possible extension of this data for large values using a technique called Reproducing Kernel Hilbert Spaces (RKHS), which is a widely used method for statistical learning.

"First, one uses tick price data to estimate the volatility of the asset in question for various levels of the asset's price," Protter explains. "Then, a special technique (RKHS with an optimization addition) is employed to extrapolate this estimated volatility function to large values for the asset's price, where this information is not (and cannot be) available from tick data. Using this extrapolation, one can check the rate of increase of the volatility function as the asset price gets arbitrarily large. Whether or not there is a bubble depends on how fast this increase occurs (its asymptotic rate of increase)."

If it does not increase fast enough, there is no bubble within the model's framework.

The authors test their methodology by applying the model to several stocks from the dot-com bubble of the nineties. They find fairly successful rates in their predictions, with higher accuracies in cases where market volatilities can be modeled more efficiently. This helps establish the strengths and weaknesses of the method.

The authors have also used the model to test more recent price increases to detect bubbles. "We have found, for example, that the IPO [initial public offering] of LinkedIn underwent bubble pricing at its debut, and that the recent rise in gold prices was not a bubble, according to our models," Protter says.

It is encouraging to see that mathematical analysis can play a role in the diagnosis and detection of bubbles, which have significantly impacted economic upheavals in the past few decades.

Robert Jarrow is a professor at the Johnson Graduate School of Management at Cornell University in Ithaca, NY, and managing director of the Kamakura Corporation. Younes Kchia is a graduate student at Ecole Polytechnique in Paris, and Philip Protter is a professor in the Statistics Department at Columbia University in New York.

Professor Protter's work was supported in part by NSF grant DMS-0906995.

Recommend this story on Facebook, Twitter,
and Google +1:

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Story Source:

The above story is reprinted from materials provided by Society for Industrial and Applied Mathematics.

Note: Materials may be edited for content and length. For further information, please contact the source cited above.

Journal Reference:

Robert Jarrow, Younes Kchia, and Philip Protter. How to Detect an Asset Bubble. SIAM J. Finan. Math., 2011; 2, pp. 839-865 [link]

Note: If no author is given, the source is cited instead.

Disclaimer: Views expressed in this article do not necessarily reflect those of ScienceDaily or its staff.

View the original article here

New technology could inspire brain implant for detecting and treating seizures

ScienceDaily (June 2, 2011) — Tiny electrodes have been coated with a drug-loaded polymer in an attempt to design an implant capable of detecting a number of neurological symptoms, such as those associated with an epileptic seizure, and treating them simultaneously.

In a study published June 2, 2011 in IOP Publishing's Journal of Neural Engineering, researchers have developed a novel technology to precisely modulate individual neurons in rats, allowing the molecular, neuronal, and circuit functions to be analysed with unprecedented precision.

Based on the electrical conducting properties of the polymer Polypyrrole (PPy), the researchers, from the University of Pittsburgh, have demonstrated a novel way of loading specific drugs onto an array of electrodes and triggering their release into cultured neurons, allowing for a more precise insight into the cellular mechanisms of neuronal networks.

On top of this, the researchers have also demonstrated how the release of drugs could be informed, in real-time, by the recording of activity in neurons, a step essential for creating a closed-loop system that both diagnoses and treats symptoms simultaneously, creating several potential applications.

Co-author Professor X Tracy Cui said, "We envision an implanted device in the future that will monitor the brain activity, detect or predict an onset of epileptic seizure, and send the command to the electrode at the most appropriate location, releasing an anti-convulsive drug to prevent the seizure."

Multielectrode arrays (MEAs) -- small devices that can control or record the electrical circuitry in neurons -- have long been used as a way of measuring neuronal activity and transforming this into an action; technologies such as ear implants and cardiac pacemakers have benefited from them.

Recent advances, however, have allowed MEAs to be coupled with devices that release specific drugs in order to test how neural circuits function, as well as investigating the underlying mechanisms within neuronal cells.

The researchers coated PPy, containing all of the necessary neurochemicals, onto an MEA. Whilst positioned on the cultured rat brain, the polymer was electrically stimulated, causing the neurochemicals to dissociate and diffuse away to the necessary locations.

Results showed that the drugs retained their activity and function with spatial and temporal precision.

Current state-of-the-art drug delivery methods, such as picospritzer and ionotopheriesis, give researchers a greater understanding of cellular mechanisms of neural dynamics; however, both of these techniques are limited to a few sites and face the risk of drug leakage.

By having the required neurochemicals dissociate from the polymer, this technique avoids the need for an external reservoir containing the drug, which would greatly increase the size of a potential implant and could cause tissue damage.

Professor Cui continues, "By directly loading a drug of interest onto an individual electrode site and using an electrical signal to trigger its release, we can precisely control the drug delivery site with ease. Additionally, our technology can be used for a combination of exogenous chemicals such as subtype-specific receptor antagonists, thus potentially allowing for more precise dissection of neural circuit function at the molecular level."

Story Source:

The above story is reprinted (with editorial adaptations by ScienceDaily staff) from materials provided by Institute of Physics, via EurekAlert!, a service of AAAS.

Journal References:

Stauffer et al. Rapid modulation of local neural activity by controlled drug release from polymer-coated recording microelectrodes. J. Neural Eng., 2011 [link]Stauffer et al. Rapid modulation of local neural activity by controlled drug release from polymer-coated recording microelectrodes. Journal of Neural Engineering, 2011; [link]

Note: If no author is given, the source is cited instead.

Disclaimer: This article is not intended to provide medical advice, diagnosis or treatment. Views expressed here do not necessarily reflect those of ScienceDaily or its staff.

View the original article here