1.Prove that, in the absence of arbitrage opportunities, the price
of a call option is a decreasing and convex function of the strike price.
2.Consider a two-period stock market with three states of the
world, and a single stock with revenue vector [ 5 3 1 ]. Show that by introducing
two call options on the stock, with different strike prices K1 and
K2, it is possible to make the market complete. What happens if the revenue
vector is [ 5 3 3 ]? Suppose now that there are four states of the world
and two assets with revenue vectors [ 1 1 2 2 ] and [ 1 2 1 2 ]. Show
that it is not possible to make the market complete by introducing one call
option for each stock. Construct a portfolio z of these two stocks such that
there exist two call options on this portfolio, with different strike prices K1
and K2, that make the market complete. |
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