### Hedge ratio with nonlinear cointegration

Posted: **August 26th, 2013, 9:07 am**

by **chocolatemoney**

Hi,Let's say we have a nonlinear cointegrating relationship y = f(x) where x is a vector of independent tradable variables (f.ex shares).I am new to non-linear cointegration. How would you calculate the hedge ratios?I could just linearize f(x). Is there something I should take into account, on top of the numerical accuracy?Which methodology would you employ?Thanks!

### Hedge ratio with nonlinear cointegration

Posted: **August 27th, 2013, 4:28 pm**

by **AnalyticalVega**

The whole idea of non-linear cointegration seems a bit silly. Yes markets are non-linear, but if your linear approx (i.e OLS). doesn't estimate well (and in many cases it won't work very well), why think a non-linear one will work better? There are an infinite number of different non-linearities..just saying..

http://cowles.econ.yale.edu/P/cp/p13b/p1355.pdf
### Hedge ratio with nonlinear cointegration

Posted: **August 28th, 2013, 5:28 am**

by **chocolatemoney**

Well, in my case, the choice of the functional form has a clear financial and economic meaning.Now it is time to numerically, locally linearize the outcome, so I can figure out the hedge ratios.Just trying to brainstorm if high school algebra does the job or if I am missing something..Anyway, thanks for the link.