Question

Show that when $f$ and $g$ provide income at rates $q_f$ and $q_g$, respectively, equation (28.15) becomes $f_0=g_0 e^{\left(q_f-q_g\right) T} E_g\left(\frac{f_T}{g_T}\right)$ (Hint: Form new securities $f^$ and $g^$ that provide no income by assuming that all the income from $f$ is reinvested in $f$ and all the income in $g$ is reinvested in $g$.)

   Show that when $f$ and $g$ provide income at rates $q_f$ and $q_g$, respectively, equation (28.15) becomes 
$f_0=g_0 e^{\left(q_f-q_g\right) T} E_g\left(\frac{f_T}{g_T}\right)$
(Hint: Form new securities $f^*$ and $g^*$ that provide no income by assuming that all the income from $f$ is reinvested in $f$ and all the income in $g$ is reinvested in $g$.)

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Options, Futures, and Other Derivatives

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 28, Problem 8

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Step 1

To do this, we assume that all the income from $f$ is reinvested in $f$ and all the income from $g$ is reinvested in $g$. This means that the new securities $f^*$ and $g^*$ will have the following income rates: $q_{f^*} = 0$ (no income from $f^*$) $q_{g^*} = 0$ Show more…

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Show that when $f$ and $g$ provide income at rates $q_f$ and $q_g$, respectively, equation (28.15) becomes $f_0=g_0 e^{\left(q_f-q_g\right) T} E_g\left(\frac{f_T}{g_T}\right)$ (Hint: Form new securities $f^*$ and $g^*$ that provide no income by assuming that all the income from $f$ is reinvested in $f$ and all the income in $g$ is reinvested in $g$.)

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