Fina $6276$ Spring $2024$

This assignment is due on April $1,2024$ by $11$ pm DC time.

Any late assignment will not be graded and will be assigned a zero.

This is an individual assignment. You can use books, internet, and class notes.

You cannot speak with any one about this assignment. No texting.

Send your answers by email.

All questions are equally weighted.

$1)$ You have three European $3-$Month XYZ calls with exercise prices $100,120$ and $130.$

The calls are at $$8,5$ and $3,$ respectively. Do you see any arbitrage opportunity?

Justify your answer.

$2)$ You have XYZ trading at $$42.$ European $6-$month $40$ calls and puts are traded at:

call put

bid$/$ask $5/5\mathrm{.}52\mathrm{.}75/3\mathrm{.}25$

Assuming the risk free rate is $0\%,$ do you see any arbitrage opportunity? Justify your answer.

$3)$ Show that options are riskier than the underlying assets.

$4)$ You have a project valued at $200$ that could increase or decrease by $25\%$ per period for two periods.

The project has three embedded options: $1.$ option to abandon at $190$;

$2.$ a contraction option with a strike of $50$ with an $80\%$ of original value; and

$3.$ an expansion option with a strike of $70$ with $130\%$ of original value.

The risk free rate is $5\%$ and the WACC is $10\%.$

What is the value of all the options combined?