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VaR_Spec__Process_TypeProcess Type refers to List of various types indicating the stochastic process followed by the respective simulated risk factor.
In all cases, the indicated stochastic process produces the future value of the referenced risk factor by applying the discretized form of its defining SDE on the initial value.
This is achieved by assuming all coefficients as being constant during each elementary time step.
For example, if the risk factor x is lognormally diffused according to dx = μxdt + σxdw, where μ, σ are constants, and the elementary time step is one week, i.e. dt = 1/52, then an initial value of x(0) within one week will evolve to x(1/52) = x(0) + μx(0)dt + σx(0)dw
This is a good approximation as long as the elementary step dt is small enough.
The size of the elementary step dt is controlled by the inputs Key VaR Spec::Actual Horizon and Key VaR Spec::Time Steps and can be done arbitrarily small by increasing the Time Steps
Available Process Type types:
The simulated risk factor follows a diffusion that is fully specified by a separate entry (object of type Stoch Process) in the last column of this table.
The simulated risk factor x follows a lognormal diffusion of the type Geom Brownian Process that has the SDE:
dx = μxdt + σxdw
The drift μ and vol σ must be supplied in the columns titled #Drift and #Vol of the table Key VaR Spec::Simulated Market
Although not required, this setting is usually accompaqnied by a VaR Spec::Modelled Factor setting of VaR Spec::Modelled Factor::Multiplier
The simulated risk factor x follows a normal diffusion of the type OU Process that has the SDE:
dx = θ(μ-x)dt + σdw
with the additional constraint that μ = 0 (mean reversion level of 0), θ = -DRIFT and σ = -VOL, where DRIFT and VOL are numbers supplied by the user in the columns titled #Drift and #Vol of the table Key VaR Spec::Simulated Market
The final equation in terms of the user-supplied DRIFT and VOL is:
dx = DRIFT*x*dt + VOL*dw
Although not required, this setting is usually accompaqnied by a VaR Spec::Modelled Factor setting of VaR Spec::Modelled Factor::Shift