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ISE 563 Financial Engineering
Homework 5
Fall 2014
Due end December 3, 2014.
1. Show that if {Bt , t = 0} is a SBM, and
a) Yt = Bt2 , then {Yt , t = 0} is referable a Martingale.
1 2
t}
b) Yt = e{c Bt – 2 c
, then {Yt , t = 0} is a Martingale.
c) Use sever (b) and the Martingale Stopping theorem to confront E[Yt ].
2. Let {Bt , t = 0} be a SBM. What is the disposal of Bs Bt , s < t? Hint: transcribe 2Bs Bt - Bs 3. Suppose the figure of a fund distribute follows a geometric Brownian agitation with purpose µ = 0.05 and volatility s = 0.3. The general figure is $95. There is a ole non-interference with practice figure $100 that expires in three months. What is the presumption that the ole non-interference has figure 0 at the span of expiration? Assume a abandon unoccupied rate r = 0.04. 4. A fund figure follows a geometric Brownian agitation with expected repay µr = 16% and volatility s = 35%. General figure is $38. Consider an European non-interference with practice figure of $40 and expiration in six months. What is the presumption that the non-interference obtain be practiced if it is a (a) ole non-interference? (b) place non-interference? ... Purchase exculpation to understand full attachment

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