Class GJRGARCHProcess

parameters supplied should be daily constants they are annualized by setting the parameter daysPerYear This class describes the stochastic volatility process governed by $$ \begin{array}{rcl} dS(t, S) &=& \mu S dt + \sqrt{v} S dW_1 \ dv(t, S) &=& (\omega + (\beta + \alpha * q_{2}

• \gamma * q_{3} - 1) v) dt + (\alpha \sigma_{12}
• \gamma \sigma_{13}) v dW_1
• \sqrt{\alpha^{2} (\sigma^{2}{2} - \sigma^{2}{12})
• \gamma^{2} (\sigma^{2}{3} - \sigma^{2}{13})
• 2 \alpha \gamma (\sigma_{23} - \sigma_{12} \sigma_{13})} v dW_2 \
  N = normalCDF(\lambda) \ n &=& \exp{-\lambda^{2}/2} / \sqrt{2 \pi} \ q_{2} &=& 1 + \lambda^{2} \ q_{3} &=& \lambda n + N + \lambda^2 N \ \sigma^{2}{2} = 2 + 4 \lambda^{4} \ \sigma^{2}{3} = \lambda^{3} n + 5 \lambda n + 3N
• \lambda^{4} N + 6 \lambda^{2} N -\lambda^{2} n^{2} - N^{2}
• \lambda^{4} N^{2} - 2 \lambda n N - 2 \lambda^{3} nN
• 2 \lambda^{2} N^{2} \
  \sigma_{12} = -2 \lambda \ \sigma_{13} = -2 n - 2 \lambda N \ \sigma_{23} = 2N + \sigma_{12} \sigma_{13} \ \end{array} $$