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In a simple regime switching model with n states, the volatility can take n values
σ1,
,σn. The volatility is selected according to a state index i(t) ∈ [1,
,n],
and the dynamics for the index is specified by the transition probabilities
p(i → j). The probabilities obey the condition ∑
j p(i → j) = 1. In a given state
i, the price follows a random walk (with Gaussian or Student innovations) with
constant volatility σi.
These figures correspond to a process with 2 states, with the parameters:
