Problem $2$ Suppose that a stock is currently trading at $$100$ per share, and the stock

price can only take two possible values one year from now: it can either go up by $20\%$ or

down by $20\%.$ The annual risk$-$free rate is $10\%.$ Assume that the stock pays no dividends.

At time zero you have $$20$ and you decide to invest all your money into buying one straddle

$($a position that consists of one long Call option and one long Put option on the same stock,

with the same strike and time to maturity$)$ that expires in $1$ year.

$($a$)$ What is the strike of this straddle $($that is$,$ what is the strike of the options in this

straddle$)?$ Assume that the strike is less than $$120.$

$($b$)$ What is the price of the Call option with the stike that you computed above?

${?}^1$ You can submit the assignment in one of the following formats: doc, docx, pdf$,$ txt$.$ Notice that MS

Excel is NOT a text editor.

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Problem Set $4$

$($c$)$ In the risk$-$neutral world $($i$.$e$.,$ under the probabilities $(q,1-q)$ that you computed

above when solving part $($a$),$ using the assumptions that we discussed in class$),$

what is the most profitable investment, a straddle, a risk$-$free bank account, or a

call option? Bonus question: Why?