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R19.P1.T3.FIN_PRODS_HULL_Ch26_ExoticOptions_Topic:Exchange-Options

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In reference to R19.P1.T3.FIN_PRODS_HULL_Ch26_ExoticOptions_Topic:Exchange-Options:-
I am trying to understand what the section circled in red means.

I have understood Exchange Options and their Payoff formula and also the pricing formula but not quite sure why:-
Min ( Ut, Vt) = Vt - Max ( Vt - Ut , 0 ) and
Max ( Ut, Vt) = Ut + Max ( Vt - Ut , 0 )
--especially in the scenario when Vt > Ut, specifically, why are we subtracting the PayOff of the Exchange Option from Vt to get the Min( Ut, Vt). Also why are we adding the PayOff of the Exchange Option TO Ut to get the Max( Ut, Vt)...? :-( :-(


Please Help !!! :-( :-(

upload_2017-2-27_0-57-17.png
 
Last edited:

ShaktiRathore

Well-Known Member
Subscriber
#2
Hi,
Vt > Ut => Min ( Ut, Vt) = Ut
Vt - Max ( Vt - Ut , 0 ) = Vt -(Vt- Ut) = Ut
hence, Min ( Ut, Vt) =Vt - Max ( Vt - Ut , 0 )

to prove,Max ( Ut, Vt) = Ut + Max ( Vt - Ut , 0 )
Vt > Ut => Max(Ut,Vt)=Vt
Ut+ Max ( Vt - Ut , 0 ) = Ut+ Vt - Ut=Vt
 
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