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The relation between volume and the price dynamics (via volatility and jumps), has been explored by various academic papers. Just cite this one and its contained references: Wang, T., & Huang, Z. (2012). The relationship between volatility and trading Volume in the Chinese Stock Market: A volatility decomposition perspective. Annals of Economics and ...


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There are two answers to your question If you want to use the Neston-Nandi model, you can use it directly with the parameters that you already show above: model = list(omega = 0.000001, alpha = 0.5, beta = 0.4) In r, the fOptions package has an HN model that can use them: HNGOption(TypeFlag, model, S, X, Time.inDays, r.daily) If you want to calculate ...


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Based on Ito's isometry, \begin{align*} E_t (r^2_{t+1}) &= E_t \bigg(\int_t^{t+1} \sigma_s dW_s \int_t^{t+1} \sigma_s dW_s\bigg)\\ &= E_t \bigg(\int_t^{t+1} \sigma_{\tau}^2 \,d\tau\bigg) \\ &= E_t\bigg(\int_0^1 \sigma_{\tau+t}^2 \,d\tau\bigg) \\ &=\int_0^1 E_t\big(\sigma_{\tau+t}^2\big) \,d\tau. \end{align*} The identity \begin{align*} E_t ...



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