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1 9 . E . 6 ? There are two dates: At date 1 there are three states; at date 0 there is trade in
E There are two dates: At date there are three states; at date there is trade in assets.
There are two basic assets whose return vectors in current dollars are
and
The market prices of these assets are and respectively. In the following you
are asked to price by arbitrage a variety of derived assets.
a Suppose that one unit of a derived asset is described as "One unit of this asset confers
the right to buy one unit of asset at of its spot value in period after the state of the
world occurs Write the return vector of this asset and price it
b The situation is the same as in a except that the asset is modified to read "One
unit of this asset confers the right to buy one unit of asset at of its spot value in period
after the state of the world occurs provided the spot value is at least
c Suppose that the asset is as in b except that at least is replaced by at least
Write down the return vector and argue that this asset cannot be priced by arbitrage with the
available primary assets.
d How would the analysis in c differ if we had in addition a riskless asset with a price
equal to You do not need to compute the price explicitly.
e Suppose that now the asset is further complicated to read "One unit of this asset confers,
at the choosing of the holder, either dollar in period or the right to buy one unit of asset
at of its spot value in period after the state of the world occurs Write the return
vector of this asset and price it
f The situation is the same as in e except that the asset is modified to read "One unit
of this asset confers, at the choosing of the holder, either dollar in period or the right to
buy one unit of asset at of its spot value in period after the state of the world occurs
provided this value is at least
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