[R-SIG-Finance] Ornstein-Uhlenbeck

[Paul Teetor]

Stephen:

I do mean-reversion trading, and I use a half-life analysis to judge the
wisdom of a trade. If the estimated half-life is too long, it doesn't make
sense to take the trade. It's a time-vs-risk thing.

In the past, I used the log(2)/speed formula mentioned by Bjorn, below. (His
link is very useful, BTW.) However, I was very unhappy with the estimates
provided by that formula. They did not match my actual trading experience.

I did some research on the topic, and got some useful results. I added a
momentum term to my model, measuruing the current slope of the spread. The
slope answers an important question: is the spread currently reverting
(moving towards the mean) or is it averting (moving away from the mean)? The
half-life is different, depending upon the current phase (reversion vs.
aversion). I found this conditioning term was statistically significant, so
I condition my estimate on it. I generate historical data and partition it
according to the market's reversion/aversion state. The two partitions shows
a different half-life, with the reverting phase having a (much) shorter
half-life than the averting phase. Both phases show an exponentally
distributed half-life, but with different means. I use those historical
estimates now in my trading, instead of the O-U estimate.

In retrospect, the problem with the O-U model is that it assumes the
mean-reverting process is always reverting. That is not quite correct. In my
experience, the spreads can alternate between periods of mean-aversion and
mean-reversion.

I hope that helps (and I hope it makes sense!).

Paul


-----Original Message-----
From: r-sig-finance-bounces at stat.math.ethz.ch
[mailto:r-sig-finance-bounces at stat.math.ethz.ch] On Behalf Of Bjorn Skogtro
Sent: Tuesday, October 12, 2010 5:34 AM
To: r-sig-finance at stat.math.ethz.ch
Subject: Re: [R-SIG-Finance] Ornstein-Uhlenbeck

Hi Stephen,

You could take a look at

http://sitmo.com/doc/Calibrating_the_Ornstein-Uhlenbeck_model

for the linear regression method, or take a look at the package "sde" which
contains some examples using GMM (not for the Ornstein-Uhlenbeck process,
though, only the CIR).

The half-life is given as log(2)/mean-reversion speed.

Do keep an eye on the partition of the time-axis, e.g. what frequency you
are using (daily, yearly) for interpreting the half-life.

BR,
Bjxrn






> ------------------------------
>
> Message: 2
> Date: Tue, 12 Oct 2010 05:43:32 -0400
> From: Sarbo <cmdr_rogue at hotmail.com>
> To: r-sig-finance at stat.math.ethz.ch
> Subject: Re: [R-SIG-Finance] Ornstein-Uhlenbeck
> Message-ID: <BLU0-SMTP21220AA5FD288F890EED317E2540 at phx.gbl>
> Content-Type: text/plain; charset="utf-8"
>
> By half-life, do you mean the speed of mean-reversion?
>
> If so, there's a bit of algebraic tomfoolery that's required to 
> discretise the equation and then fit the data to it. I don't have the 
> time right now to go into all the details but it's not hard- you can 
> parameterise the process using simple linear regression. If you need 
> help with that I'll try and get back to you tonight about it.
>
> On Tue, 2010-10-12 at 13:47 +1100, Stephen Choularton wrote:
>
> > Hi
> >
> > Wonder if anyone could point me how I use this method to discover 
> > the half life of a mean reverting process.
> >
> > I am looking into pair trading and the time it takes for a 
> > cointegrated pair to revert to the norm.
> >
> > --
> > Stephen Choularton Ph.D., FIoD
> >
> > 9999 2226
> > 0413 545 182
> >
> >
> > for insurance go to www.netinsure.com.au for markets go to 
> > www.organicfoodmarkets.com.au
> >
> >
> > _______________________________________________
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