en>Lambiam: f_2 should not occur in the limit since it equals f_1 g_1 f_1

2013-10-20T17:51:34Z

f_2 should not occur in the limit since it equals f_1 g_1 f_1

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{{multiple issues|
{{Notability|date=June 2013}}
{{primary sources|date=December 2012}}
}}

'''Cointelation''' is a [[portmanteau]] neologism in finance, designed to signify a hybrid method between [[cointegration|COINTegration]] and [[correlation|corrELATION]] techniques.

Correlation is typically used by financial practitioners, when representing relationships between assets. However, academics have long since questioned this method due to the plethora of issues that plague it related to [[spurious correlation]]. Academics often think cointegration is a natural replacement in some of the cases as it is able to represent the physical reality of these assets better. However, despite this general academic consensus, cointegration is not widely used by financial practitioners.<ref name="wilmott.com">{{cite journal|authors=Mahdavi Damghani B., Welch D., O'Malley C., Knights S.|title=The Misleading Value of Measured Correlation |journal=Wilmott Magazine|year=2012|url=http://wilmott.com/pdfs/MVMC_CSL_05_2012.pdf}}</ref> So in 2012 Babak Mahdavi Damghani, Daniella Welch, Ciaran O'Malley and Stephen Knights proposed a hybrid method to encourage financial practitioners to begin to utilise cointelation as a superior alternative to both correlation and cointegration. The cointelation relationship can be described by the following set of [[Stochastic differential equation]]:

<math> \frac{dS_{t}}{S_{t}} = r dt + \sigma dW_t</math>

<math>dS_{l,t} = \theta (S_{t}-S_{l,t})dt + \sigma S_{l,t} \left(\rho dW_t + \sqrt{1-\rho^2}dW_t^\bot\right)</math>

<math>S_{t}</math> is commonly referred to as the leading stochastic process and <math>S_{l,t}</math> the lagging stochastic process. With this dynamical system, if the correlation of cointelation <math>\rho</math> is set to -1, conditional to the time lapse between returns measurements, then the measured correlation one gets can span the whole correlation range [-1,1].

[[File:Cointelation and measured correlation.pdf|thumb|Cointelation and measured correlation]]

The particular point of cointelation can be linked to the concept of Inferred Correlation <ref name="wilmottM.com">{{cite journal|authors=Mahdavi Damghani B.|title=The Non-Misleading Value of Inferred Correlation: An Introduction to the Cointelation Model|journal=Wilmott Magazine|year=2013|url=http://onlinelibrary.wiley.com/doi/10.1002/wilm.10252/abstract}}</ref> which gives an expectation of the maximum measured correlation of cointelated pairs at timescale not measurable:

<math>E[\sup \rho_{t}] = \rho + (1-\rho)(1-e^{-\lambda \theta (t-1)}) </math> where <math>\rho</math> and <math>\theta</math> are the parameters from the cointelated SDE.

==See also==
*[[Correlation]]
*[[Cointegration]]
*[[Stochastic differential equation]]

==References==
{{reflist}}

[[Category:Econometrics]]
[[Category:Financial risk]]

{{finance-stub}}

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en>Lambiam: f_2 should not occur in the limit since it equals f_1 g_1 f_1