Construct a portfolio consisting of risk$-$free bonds, European call and put options to replicate the payoff function X$($S$)$

below. Be specific about how many options of each type are in your portfolio.

Use $+$ sign if you buy option and $-$ sign if you short it$.$ Use $0$ if you do not use an option.

$x(S)=\{\begin{array}{ccc}3S-90,& \text{S}\text{i}\text{n}[0,& 30)\\ 90-3S,& \text{S}\text{i}\text{n}[30,& )\end{array}$

Enter number of the options you will use with the given characteristics if bonds are not available.

Note that the grader will mark your answer as correct only if all provided numbers are correct.

Call Options with Strike $=30$

Some of the numbers might be correct, but your portfolio has a different payoff.

Call Options with Strike $=20$

Some of the numbers might be correct, but your portfolio has a different payoff.

Call Options with Strike $=10$

Put Options with Strike $=10$

Some of the numbers might be correct, but your portfolio has a different payoff.

Put Options with Strike $=30$

Some of the numbers might be correct, but your portfolio has a different payoff.