a) A derivative contract has the following payo at maturity: fT = erT ln ST , where
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Question:
a) A derivative contract has the following payo at maturity:
fT= erT ln ST ,
where r is a constant interest rate.The underlying asset is described by the following process (under the real world probability),
dS = Sdt + Sdz ,
where, , andare constants, and z is a Wiener process. Show that, when r = 0
2
the price at time zero of the derivative contract is, f0= lnS01
2T .
(b) Optional. Apply Ito's lemma to the following functions:
(i) X = z2
(ii) Y = t2 + ez
where, z is Wiener process, and t represents time.
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