(a) Find the price and the hedging portfolio of a contract V that pays off the best asset out of X,.

(a) Find the
price and the hedging portfolio of a contract V that pays off the best asset
out of X, K1Y , and K2Z, or in other words VT = max(XT , K1YT , K2ZT ) where
the prices of the underlying assets follow geometric Brownian motion models
given by s (8.8), (8.9), and (8.10). As an immediate consequence, find the
price and the hedge for the call option on the best of two assets with the
payoff (max(XT , K1YT ) − K2ZT ) +. (b) Find the price and the hedging
portfolio of a contract that pays off the worst asset min(XT , K1YT , K2ZT ).
(c) Find the price and the hedging portfolio of a contract that pays off the
“middle” asset, which can be defined as XT + K1YT + K2ZT − max(XT , K1YT
, K2ZT )− min(XT , K1YT , K2ZT )