Time$-$to$-$expiration $($days$)$: $42$ days Underlying asset price: $80$ Risk$-$free interest rate: $4\mathrm{.}5\%$ Income from underlying assets: No $($a$)$ If the calls and puts are European$-$style options, what are the lower and upper bounds of the options with strike prices of $79$ and $82?(8$ marks$)($b$)$ If the calls and puts are American$-$style options, what are the lower and upper bounds of the options with strike prices of $79$ and $82?(8$ marks$)2($c$)$ Comment on the boundary conditions of American and European options. $(6$ marks$)($d$)$ State the factors affecting your choice of American versus European options.