Consider an economy with dates t $=0,1$ and S $=3$ states at

date t $=1.$ A risky security A has payoff $(60,60,90)$ and has equilibrium price

PA $=80.$ A risk$-$less security B has payoff $(100,100,100)$ and has equilibrium

price pB $=100.$

$($a$)$ Assuming the absence$-$of$-$arbitrage principle, find bounds on the price of

call option on A with strike z $=75.$

$($b$)$ Assume now that the also the call option given above is traded at the price

pCO$($A$,75).$ State whether the market with A$,$ B$,$ and the call is complete.

$($c$)$ Assume further that pCO$($A$,75)=8.$ Give the definition of strong arbitrage

and, if possible, find one