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Long-Memory-Affine-Microscopic ARCH process with relative returns

The price update equation uses relative returns (see the description for the GARCH process)

The volatility part is identical to the LM-Aff-Mic-ARCH process.

The parameters for the simulations are identical to the corresponding process with logarithmic return:

• σ∞ = 0.11
• w∞ = 0.068
• λ = 0
• ρ =
• τ₀ = exp(-4) day = 26 min
• ρ^n-1 = 1024 (i.e. n = 21)

The innovations have a Student distribution with 3.3 degree of freedom. The simulation time corresponds to 200 years with a time increment δt = 3 minutes.