# [R-SIG-Finance] Vasicek model estimation via linear regression

Zanella Marco marco.zanella at inbox.com
Wed Jun 17 18:41:27 CEST 2009

```Hi,
I have to check mean reversion with a Vasicek model for a time series. As you certainly know Vasicek process is discribed by following formula:

dXt = a(b-Xt)dt + sdWt   (1)

http://en.wikipedia.org/wiki/Vasicek_model

To estimate the parameters in my data I can use this expression:

Xt - Xt-1 = a(b-Xt-1)Dt + se   (2)

where:
Xt: time series at time t
Xt-1: time series at time t-1
a: unknown parameter
b: unknown parameter
Dt: in my case I can assimilate it = 1
S: standard deviation
e: error ~N(0,1)

Basically, I want to estimate unknown parameters a and b using a linear regression. Usually I work on linear regression with lm() function but I don't undertand how formulate my (2) model in to lm command. Can anyone give me some suggestions?

Thanks in advance.

Regards,

Marco

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