create new multi-regime stochastic process
RegimeSwitchingProcess(P, S, i, n, t)
Matrix; transition matrix
posint; initial state
posint; number of states per year
name; time variable
The RegimeSwitchingProcess command creates a regime-switching process with the specified regimes and transition probability. Each of the regimes must be a one-dimensional stochastic process. The parameter S defines all possible regimes that are one-dimensional stochastic processes. Moves between different regimes are assumed to be governed by the d×d transition probability matrix, P, with generic element Pj,k defined as the probability of moving from regime k to regime j.
The parameter n is the number of regimes per year. This process can only be simulated with m time steps per year, where m is a multiple of n. Assume for example that X is a finite state Markov chain with 3 regimes per year. If we simulate the process X on the interval 0..2 with 12 time steps, then the regime change can occur only at steps 2, 4, 6, 8, and 10.
Consider a regime switching process with 2 regimes. In the first regime, the process is a Brownian motion with zero drift and high volatility; in the second regime, the process behaves like a Brownian motion with hight drift and low volatility. The transition probabilities are: 0.5 for moving to the second regime given that the process is in the first regime and 0.2 for moving to the first regime given that the process is in the second regime. The process will have 2 regimes per year, which means that the regimes can switch only at t=0.5, t=1.0, and t=1.5.
P ≔ 0.5,0.5|0.2,0.8
S ≔ BrownianMotion⁡0,0,2.0,BrownianMotion⁡0,0.5,0.001:
X ≔ RegimeSwitchingProcess⁡P,S,1,2:
The second example is similar to the one above, but one of the processes is deterministic.
S ≔ BrownianMotion⁡0,0,2.0,0.5⁢t
X ≔ RegimeSwitchingProcess⁡P,S,1,2,t
The Finance[RegimeSwitchingProcess] command was introduced in Maple 15.
For more information on Maple 15 changes, see Updates in Maple 15.
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