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I have a stochastic volatility model for commodity price which follows an AR(1) process:

ln(pt ) − m = ρ (ln(pt−1) − m) + exp(σt)ut ut ∼ IID(0, 1) σt − μ = ρσ(σt−1 − μ) + ηεt εt ∼ IID(0, 1)

After estimating the above process, I use the estimated parameters to solve a small open economy model where the price of a commodity depends on its time varying level as well as volatility. I have 7grids for price level and 5 grids for discretizing the volatility states, so that the price matrix is of dimension (7 by 5). However, when I use rowenhorst to discretize the above price process, the transition matrix looks same for all the volatility levels. Is it normal? I don't understand why the transitions of moving from one price level to another remain same at different levels of volatility. Here is how the (7x7x5) transition matrix for price looks like. The last column in the matrix refers to the volatility levels. enter image description here

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  • $\begingroup$ Consider whether this might be a better fit for Cross Validated Stack Exchange, as there may be more users with expertise in models like yours. (I am not sure.) $\endgroup$
    – Richard Hardy
    Jun 10 at 10:39

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