[R-SIG-Finance] State-dependent volatility in state space model - CIR

Kristian Lind kristian.langgaard.lind at gmail.com
Mon Nov 14 22:39:07 CET 2011


Just to clarify, the model I want to estimate is the state space
version of the Cox-Ingersoll-Ross model.

2011/11/14 Kristian Lind <kristian.langgaard.lind at gmail.com>:
> Hi everyone,
>
> I posted a similar question on the R-help list a few days ago and it
> was suggested to me to try here instead. I apologize for the
> cross-posting.
>
> I'm trying to model a term structure of yield spreads where the state
> variables are independent square-root processes.
>
> The state space model I want to estimate using a Kalman filter takes
> the following form -
>
> measurement eq:
>
> z_t = a + b*y_t + eps_t
>
> transition eq
>
> y_t+h = (I -exp(-hL))theta + exp(-hL)y_t+ eta_{t+h}.
>
> The problem is that the distribution of the error terms of the
> transition equation depend on the previous value of the state
> variable.
> To be exact: y_t|y_{t-1} ~N(mu, Q_t) where Q is a diagonal matrix with
> elements equal to
>
> Q_{i,t} = sigma_i*(1-exp(-kappa_i*h)/kappa_i*(theta_i/2*(1-exp(kappa_i*h)+exp(-kappa_i*h)y_{t-1,i}
>
> I found an old thread about the same problem
> https://stat.ethz.ch/pipermail/r-sig-finance/2007q2/001362.html
>
> I've adapted Prof. Silva's code by to my setting, but the optimization
> process breaks down.
>
> Any ideas or examples on how to solve this problem are much appreciated.
>
> Thank you in advance.
>
> Kristian
>



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