A bear spread payoff has the form $g(S_T)=$max$(K_2-S_T,0)-$max$(K_1-S_T,0),$ where $0$

$v(t,x)={\displaystyle \underset{0}{\overset{}{}}}\frac{1}{y}K(\frac{x}{y},t,T)g(y)dyv(t,x)K1.$

$(a)$ Sketch the payoff diagram.

$(b)$ Use the general formula for the European option pricing function $to$ find the time$-$zero option

price $of$ a bear spread.

$(C)$ general formula for European option pricing $isv(t,x)={\displaystyle \underset{0}{\overset{}{}}}\frac{1}{y}K(\frac{x}{y},t,T)g(y)dy.$ Use this

formula and find $v(t,x).$