[R-SIG-Finance] Cox, Ingersoll, Ross/Vasicek parameter estimation via Kalman-Filter (SSPIR)

[Eric Zivot]

In my survey paper http://faculty.washington.edu/ezivot/statespacesurvey.pdf
, I have an example of estimating a simple Vasicek model using state space
methods in splus. With the more complicated CIR process the Kalman filter
recursions have to be modified because the state vector influences the
variance of the process.
ez

-----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 Arne Krombach
Sent: Thursday, April 26, 2007 3:02 PM
To: r-sig-finance at stat.math.ethz.ch
Subject: [R-SIG-Finance] Cox, Ingersoll,Ross/Vasicek parameter estimation
via Kalman-Filter (SSPIR)

Dear R-Users,

 

I am trying to estimate the parameters for a CIR 1-/2-/3-Factor model via
Kalman filtering. The idea was to do it via the package SSPIR, but I have
problems to transform the CIR state space form into the SSPIR syntax.
Actually, I am not quite sure if this is possible at all. 

 

Did anybody already realise a CIR/Vasicek -parameter estimation via R? 

 

To get an idea how a CIR-1-factor state space form looks like (Y= vector of
zerobond-yields with the maturities tau at month t):

 

Y(t,tau)= ( -1/tau * log A(tau) ) + (1/tau * B(tau) * x(t) + e

 

Where :

 

A(tau) = [(2 * h * e^( a + lambda + h) * tau/2) / (2 * h + (a + lambda + h)
* (e^(tau * h) - 1)] ^(2 * b/ sigma^2)

B(tau) = [(2 * (e^(tau * h)  -1)) / 2 * h + (a + lambda + h) * (e^(tau * h)
- 1)]

h = sqrt[(a + lambda)^2 + 2*sigma^2] 

 

which means that, besides the time varying factor x, the parameters a, b,
sigma, and lambda have to be estimated via Kalman filtering.

 

Is it possible to implement this in SSPIR? If you have any other suggests or
if you already implement comparable models in R, I would be very grateful
for your help.

 

Kind Regards,

 

Arne Krombach


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