Consider an economy with three future possible states of the world, call them bust, normal state,

and boom. The value of the MSCI world index in these states is respectively $\{80,100,110\}.$

Investors can trade three assets. An ETF $($Exchange Traded Fund$)$ on the MSCI world index,

whose value matches that of the index. A riskfree asset, whose state$-$by$-$state payoffs are

$\{1,1,1\}.$ A call option on the MSCI world index, with exercise price $($or strike$)100,$ so that

its payoff in any state is equal to max $\{$MSCI world index $100,0\}.$

Question B$\mathrm{.}1$ Write down the state contingent payoffs $($payoffs state$-$by$-$state$)$ of the option.

Question B$\mathrm{.}2$ Are markets complete? Prove it