(c) Let = Itô's formula we obtain the dynamic of under as Zt 1/St. Z Q where is a process. Integrate and take conditional expectation to obtain V Q-Wiener Ft] Let = | and take the derivative w.r.t. This yields the following ODE for m(u) E[Zu u. m Solving the ODE we obtain The price at time [0, of "the inverse mean" is therefore given by t T0) 5.
(c) Let Zt = 1/St. Itô's formula we obtain the dynamic of Z under Q as where V is a Q-Wiener process. Integrate and take conditional expectation to obtain Let m(u) = E[Zu | Ft] and take the derivative w.r.t. u. This yields the following ODE for m Solving the ODE we obtain The price at time t [0, T0) of "the inverse mean" is therefore given by 5.
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