[R-SIG-Finance] Ornstein-Uhlenbeck

stefano iacus stefano.iacus at unimi.it
Tue Oct 12 18:11:59 CEST 2010 

that's another point and I completely agree with you :-)

so the real point is not trying to fit wrong models on the (so to say) "wrong" data 


stefano

On 12 Oct 2010, at 18:00, Patrick Burns wrote:

> The OU process is Gaussian, but the
> market didn't get the memo that *it*
> has to be Gaussian.
> 
> On 12/10/2010 16:41, stefano iacus wrote:
>> just for completeness: OU process is gaussian and transitiion density is known in exact form. So maximum likelihood estimation works fine and I suggest to avoid GMM.
>> 
>> sde package contains exact transition density for this process (e.g. ?dcOU) which you can use to build the likelihood to pass to mle() function.
>> 
>> This example taken from the "inst" directory of the package sde. For the parametrization of the model see ?dcOU
>> 
>> 
>> # ex3.01.R
>> OU.lik<- function(theta1, theta2, theta3){
>>   n<- length(X)
>>   dt<- deltat(X)
>>   -sum(dcOU(X[2:n], dt, X[1:(n-1)], c(theta1,theta2,theta3), log=TRUE))
>>  }
>> 
>> require(stats4)
>> require(sde)
>> set.seed(123)
>> X<- sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1)
>> mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
>>       method="L-BFGS-B", lower=c(-Inf,0,0)) ->  fit
>> summary(fit)
>> 
>> # ex3.01.R (cont.)
>> prof<- profile(fit)
>> par(mfrow=c(1,3))
>> plot(prof)
>> par(mfrow=c(1,1))
>> vcov(fit)
>> confint(fit)
>> 
>> # ex3.01.R (cont.)
>> set.seed(123)
>> X<- sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1e-3)
>> mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
>>       method="L-BFGS-B", lower=c(-Inf,0,0)) ->  fit2
>> summary(fit2)
>> 
>> 
>> I hope this helps out
>> 
>> stefano
>> 
>> On 12 Oct 2010, at 12:33, Bjorn Skogtro wrote:
>> 
>>> 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,
>>> Bjørn
>>> 
>>> 
>>> 
>>> 
>>> 
>>> 
>>>> ------------------------------
>>>> 
>>>> 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
>>>>> 
>>>>> 
>>>>> _______________________________________________
>>>>> R-SIG-Finance at stat.math.ethz.ch mailing list
>>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-finance
>>>>> -- Subscriber-posting only. If you want to post, subscribe first.
>>>>> -- Also note that this is not the r-help list where general R questions
>>>> should go.
>>>> 
>>>> 
>>>> -------------- next part --------------
>>>> An HTML attachment was scrubbed...
>>>> URL:<
>>>> https://stat.ethz.ch/pipermail/r-sig-finance/attachments/20101012/26e32fc7/attachment-0001.html
>>>>> 
>>>> -------------- next part --------------
>>>> A non-text attachment was scrubbed...
>>>> Name: CoS2010Winner.JPG
>>>> Type: image/jpeg
>>>> Size: 16091 bytes
>>>> Desc: not available
>>>> URL:<
>>>> https://stat.ethz.ch/pipermail/r-sig-finance/attachments/20101012/26e32fc7/attachment-0001.jpe
>>>>> 
>>>> 
>>>> ------------------------------
>>>> 
>>>> _______________________________________________
>>>> R-SIG-Finance mailing list
>>>> R-SIG-Finance at stat.math.ethz.ch
>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-finance
>>>> 
>>>> 
>>>> End of R-SIG-Finance Digest, Vol 77, Issue 8
>>>> ********************************************
>>> 
>>> 	[[alternative HTML version deleted]]
>>> 
>>> _______________________________________________
>>> R-SIG-Finance at stat.math.ethz.ch mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-finance
>>> -- Subscriber-posting only. If you want to post, subscribe first.
>>> -- Also note that this is not the r-help list where general R questions should go.
>> 
>> 
>> -----------------------------------
>> Stefano M. Iacus
>> Department of Economics,
>> Business and Statistics
>> University of Milan
>> Via Conservatorio, 7
>> I-20123 Milan - Italy
>> Ph.: +39 02 50321 461
>> Fax: +39 02 50321 505
>> http://www.economia.unimi.it/iacus
>> ------------------------------------------------------------------------------------
>> Please don't send me Word or PowerPoint attachments if not
>> absolutely necessary. See:
>> http://www.gnu.org/philosophy/no-word-attachments.html
>> 
>> _______________________________________________
>> R-SIG-Finance at stat.math.ethz.ch mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-finance
>> -- Subscriber-posting only. If you want to post, subscribe first.
>> -- Also note that this is not the r-help list where general R questions should go.
>> 
> 
> -- 
> Patrick Burns
> patrick at burns-stat.com
> http://www.burns-stat.com
> http://www.portfolioprobe.com/blog
> 
> _______________________________________________
> R-SIG-Finance at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-finance
> -- Subscriber-posting only. If you want to post, subscribe first.
> -- Also note that this is not the r-help list where general R questions should go.


-----------------------------------
Stefano M. Iacus
Department of Economics,
Business and Statistics
University of Milan
Via Conservatorio, 7
I-20123 Milan - Italy
Ph.: +39 02 50321 461
Fax: +39 02 50321 505
http://www.economia.unimi.it/iacus
------------------------------------------------------------------------------------
Please don't send me Word or PowerPoint attachments if not 
absolutely necessary. See:
http://www.gnu.org/philosophy/no-word-attachments.html

More information about the R-SIG-Finance mailing list