Question $1[10$ points$]$

A trader buys an European call option with the strike price Kc and an European put

option with the strike price Kp$.$ The call options costs c and the put option costs p$.$

Assume that Kc $>$ Kp and c $<$ p$.$ Both options have the same maturity.

$1.$ Draw a diagram showing the trader$$s payoff at the time of maturity. $[3$ points$]$

$2.$ Compute two stock prices at which trader$$s net profit will be zero. $[3$ points$]$

$3.$ Denote the lower price Pl and higher price Ph$.$ Show that following conditions holds

$[4$ points$]$

$$Pl

$$c

$<0,$

$$Pl

$$p

$<0,$

$$Ph

$$c

$>0,$

$$Ph

$$p

$>0$