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Stochastic evolution of distributions and functional Bollinger bands

Authors: Bernis, Guillaume; Brunel, Nicolas; Kornprobst, Antoine; Scotti, Simone;

Stochastic evolution of distributions and functional Bollinger bands

Abstract

AbstractWe use mixture of percentile functions to model credit spread evolution, which allows to obtain a flexible description of indices and their components at the same time. We show regularity results in order to extend mixture percentile to the dynamic case. We characterize the stochastic differential equation of the flow of cumulative distribution function and we link it with the ordered list of the components of the credit index. The main financial goal is to introduce a functional version of Bollinger bands. The crossing of bands by the spread is associated with a trading signal. Finally, we show the richness of the signals produced by functional Bollinger bands compared with standard one with a practical example in credit asset.

Countries
Italy, France
Keywords

[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], [STAT.ME] Statistics [stat]/Methodology [stat.ME], 330, Bollinger bands, credit risk, Statistics, quantile functions, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [STAT.ME]Statistics [stat]/Methodology [stat.ME], stochastic models

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
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