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GJRGARCH_Model

The underlying price S follows the SDE:
dS = μSdt + σSdW1
where the volatility σ is a function of S and t.
Let v := σ², then:
dv = (ω + (β + αq + γQ - 1)v) dt + (ατ + γυ)vdz
+ sqrt{α² (χ² - τ²) + γ²(ψ² - υ²) + 2αγ(φ - τυ)}vdw
N = normalCDF(λ)
n = exp{-λ²/2} / sqrt{2π}
q = 1 + λ²
Q = λn + N + λ²N
χ² = 2 + 4 λ²λ²
ψ² = λ³n + 5λn + 3N + λ²λ²N + 6λ²N -λ²n² - Ν² - λ²λ²Ν² - 2λnN - 2λ³nN - 2λ²Ν²
τ = -2λ
υ = -2n - 2λN
φ = 2N + τυ
Information on the QuantLib implementation may be found in
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