Handbook of Heavy Tailed Distributions in Finance

$\begin{array}{l} r_{J D}^{*} (i + 1, j_{i + 1}) = r_{J D}^{*} (j_{i + 1}) \\ = {\begin{cases} \begin{matrix} r_{D}^{*} (j_{i}) + Δ_{u} (j_{i}, j_{i + 1}) + μ + γ, & w . prob . \frac{λ}{2} p_{u} (j_{i}), \\ r_{D}^{*} (j_{i}) + Δ_{u} (j_{i}, j_{i + 1}) & w . prob . (1 - λ) p_{u} (j_{i}), \end{matrix} \\ \begin{matrix} r_{D}^{*} (j_{i}) + Δ_{u} (j_{i}, j_{i + 1}) + μ - γ, & w . prob . \frac{λ}{2} p_{u} (j_{i}), \end{matrix} \\ \begin{matrix} r_{D}^{*} (j_{i}) + Δ_{d} (j_{i}, j_{i + 1}) + μ + γ, & w . prob . \frac{λ}{2} p_{d} (j_{i}), \end{matrix} \\ \begin{matrix} r_{D}^{*} (j_{i}) + Δ_{d} (j_{i}, j_{i + 1}), & w . prob . (1 - λ) p_{d} (j_{i}), \end{matrix} \\ \begin{matrix} r_{D}^{*} (j_{i}) + Δ_{d} (j_{i}, j_{i + 1}) + μ - γ, & w . prob . \frac{λ}{2} p_{d} (j_{i}) . \end{matrix} \end{cases} \end{array}$

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

$r_{J D}^{*} (i + 1, j_{i + 1}) = r_{J D}^{*} (j_{i + 1}) + α (i + 1),$

for any i = 0,…,M− 1 and $j_{i} \in J_{i} \cap (j_{d}, j_{u})$ .

4 The econometric analysis

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Handbook of Heavy Tailed Distributions in Finance by S.T Rachev

4 The econometric analysis

4.1 ...

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