$\begin{array}{l}{r}_{JD}^{*}\left(i+1,{j}_{i+1}\right)={r}_{JD}^{*}\left({j}_{i+1}\right)\\ =\left\{\begin{array}{l}\begin{array}{cc}{r}_{D}^{*}\left({j}_{i}\right)+{\Delta }_{u}\left({j}_{i},{j}_{i+1}\right)+\mu +\text{γ},& \text{w}.\text{prob}\text{.}\frac{\text{λ}}{2}{p}_{u}\left({j}_{i}\right),\\ {r}_{D}^{*}\left({j}_{i}\right)+{\Delta }_{u}\left({j}_{i},{j}_{i+1}\right)& \text{w}.\text{prob}\text{.}\left(1-\text{λ}\right){p}_{u}\left({j}_{i}\right),\end{array}\\ \begin{array}{cc}{r}_{D}^{*}\left({j}_{i}\right)+{\Delta }_{u}\left({j}_{i},{j}_{i+1}\right)+\mu -\text{γ},& \text{w}.\text{prob}\text{.}\frac{\text{λ}}{2}{p}_{u}\left({j}_{i}\right),\end{array}\\ \begin{array}{cc}{r}_{D}^{*}\left({j}_{i}\right)+{\Delta }_{d}\left({j}_{i},{j}_{i+1}\right)+\mu +\text{γ},& \text{w}.\text{prob}\text{.}\frac{\text{λ}}{2}{p}_{d}\left({j}_{i}\right),\end{array}\\ \begin{array}{cc}{r}_{D}^{*}\left({j}_{i}\right)+{\Delta }_{d}\left({j}_{i},{j}_{i+1}\right),& \text{w}.\text{prob}\text{.}\left(1-\text{λ}\right){p}_{d}\left({j}_{i}\right),\end{array}\\ \begin{array}{cc}{r}_{D}^{*}\left({j}_{i}\right)+{\Delta }_{d}\left({j}_{i},{j}_{i+1}\right)+\mu -\text{γ},& \text{w}.\text{prob}\text{.}\frac{\text{λ}}{2}{p}_{d}\left({j}_{i}\right).\end{array}\end{array}\end{array}$

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 $ji∈Ji∩(jd,ju)$.

## 4 The econometric analysis

#### 4.1 ...

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