Replication a options portfolio

Question

I'm not too sure I'm going about answering this question correctly.

I have used the following to derive my answer. I see that the portfolio above is a combination of a short-call(strike price 20) and a short put(strike price 30).

Answer 1

Instead of payout, think in terms of the slope of the payout (i.e the delta).

• If you long a call at $A$ and cover it by shorting a call at $B > A$,
  the slope will be $1$ between $A$ and $B$ and $0$ otherwise.

• If you long a put at $D$ and cover it by shorting a put at $C < D$,
  the slope will be $-1$ between $C$ and $D$ and $0$ otherwise.

In the payout you have, the slope is

• $-2$ between $20$ and $30$,
• $+1$ between $30$ and $40$
• and $0$ otherwise.

Since the payout is $0$ at $30$, you can replicate it by

• Long $2$ put at $30$, cover it by shorting $2$ put at $20$.
• Long $1$ call at $30$, cover it by shorting $1$ call at $40$.