Handbook of Heavy Tailed Distributions in Finance

$\begin{array}{l}{r}_{JD}^{*}\left(i+1,j_{i+1}\right)=r_{JD}^{*}\left(j_{i+1}\right)\\ =\{\begin{array}{l}\begin{array}{cc}{r}_D^{*}\left(j_i\right)+{\Delta }_u\left(j_i,j_{i+1}\right)+\mu +\text{γ},& \text{w}.\text{prob}\text{.}\frac{\text{λ}}{2}{p}_u\left(j_i\right),\\ r_D^{*}\left(j_i\right)+{\Delta }_u\left(j_i,j_{i+1}\right)& \text{w}.\text{prob}\text{.}\left(1-\text{λ}\right)p_u\left(j_i\right),\end{array}\\ \begin{array}{cc}{r}_D^{*}\left(j_i\right)+{\Delta }_u\left(j_i,j_{i+1}\right)+\mu -\text{γ},& \text{w}.\text{prob}\text{.}\frac{\text{λ}}{2}{p}_u\left(j_i\right),\end{array}\\ \begin{array}{cc}{r}_D^{*}\left(j_i\right)+{\Delta }_d\left(j_i,j_{i+1}\right)+\mu +\text{γ},& \text{w}.\text{prob}\text{.}\frac{\text{λ}}{2}{p}_d\left(j_i\right),\end{array}\\ \begin{array}{cc}{r}_D^{*}\left(j_i\right)+{\Delta }_d\left(j_i,j_{i+1}\right),& \text{w}.\text{prob}\text{.}\left(1-\text{λ}\right)p_d\left(j_i\right),\end{array}\\ \begin{array}{cc}{r}_D^{*}\left(j_i\right)+{\Delta }_d\left(j_i,j_{i+1}\right)+\mu -\text{γ},& \text{w}.\text{prob}\text{.}\frac{\text{λ}}{2}{p}_d\left(j_i\right).\end{array}\end{array}\end{array}$

Then, the hexanomial tree representing the jump-diffusion process (16) is defined by

$r_{JD}^{*}\left(i+1,j_{i+1}\right)=r_{JD}^{*}\left(j_{i+1}\right)+\alpha \left(i+1\right),$

for any i = 0,…,M− 1 and ${\mathit{j}}_{\mathit{i}}\in {\mathit{J}}_{\mathit{i}}\cap ({\mathit{j}}_{\mathit{d}},{\mathit{j}}_{\mathit{u}})$.

4 The econometric analysis

4.1 ...