Question $1[20$ points$]$

A trader buys two European call options, one with the strike price Kc$1$ and the other with

Kc$2,$ and an European put option with the strike price Kp$.$ The call option with strike

price Kc$1$ costs c$1,$ the call option with strike price Kc$2$ costs c$2,$ and the put option costs

p$.$ Assume that Kc$2>$ Kc$1>$ Kp$.$ All options have the same maturity.

$1.$ Draw a diagram showing the trader$$s payoff at the time of maturity when Kc$2$

Kc$1$ c$1$ c$2$ p $<0[3$ points$]$

$2.$ Draw a diagram showing the trader$$s payoff at the time of maturity when Kc$2$

Kc$1$ c$1$ c$2$ p $>0[3$ points$]$

$3.$ There will be two stock prices in both cases mentioned above where the trader$$s net

profit will be zero. Denote two stock price for the first case as P

$1$

l

and P

$1$

h where

P

$1$

l $<$ P$1$

h

$.$ Similarly, for the second case, denote two prices as P

$2$

l

and P

$2$

h

such that

P

$2$

l $<$ P$2$

h

$.$ Derive, P

$1$

l

$,$ P$1$

h

$,$ P$2$

l

$,$ P$2$

h

$.[7$ points$]$

$4.$ Show: $[7$ points$]$

$$P$1$

h

$$ST

$=2$ and $$P$2$

h

$$ST

$=1$