Question $1$

$[20$ Marks$]$

You create an options portfolio by selling a put option with an exercise price of $90$ while simultaneously

purchasing a put option on the same stock with an exercise price of $95.$ Both options expire on the same

date.

a$.$ Illustrate the payoff structure of this portfolio at the options' expiration date.

b$.$ On the same chart, display the portfolio's profit at expiration. Which of the two options should have

a higher premium? Briefly explain why.