$1)$ In a one$-$period binomial model, assume that the current stock price is $$105,$ and that it will rise to $$125$ or fall to $$85$ after one month. The gross return for the risk free rate of return for one period is $1\mathrm{.}015.$ Creating a replicating portfolio, what is the price of a one$-$month put option at a strike price of $$105?$

a$.$ $$6\mathrm{.}52$

b$.$ $$7\mathrm{.}93$

c$.$ $$8\mathrm{.}48$

d$.$ $$9\mathrm{.}99$

part b

From question $1,$ if the market price of the put option is $$7\mathrm{.}50($underpriced$),$ what would be the steps in creating risk free arbitrage profit?

a$.$ Sell one put with a strike of $105,$ Short $0\mathrm{.}50$ units of the stock, Invest $$60\mathrm{.}98$ for one period at the rate r $=1\mathrm{.}025$

b$.$ Buy one put with a strike of $105,$ Short $0\mathrm{.}50$ units of the stock, Invest $$60\mathrm{.}98$ for one period at the rate r $=1\mathrm{.}025$

c$.$ Sell one put with a strike of $105,$ Buy $0\mathrm{.}50$ units of the stock, Borrow $$60\mathrm{.}98$ for one period at the rate r $=1\mathrm{.}025$

d$.$ Buy one put with a strike of $105,$ Buy $0\mathrm{.}50$ units of the stock, Borrow $$60\mathrm{.}98$ for one period at the rate r $=1\mathrm{.}025$

part c

From question $1,$ if the market price of the put option is $$9\mathrm{.}25($overpriced$),$ what would be the steps in creating risk free arbitrage profit?

a$.$ Buy one put with a strike of $105,$ Buy $0\mathrm{.}50$ units of the stock, Borrow $$60\mathrm{.}98$ for one period at the rate r $=1\mathrm{.}025$

b$.$ Buy one put with a strike of $105,$ Short $0\mathrm{.}50$ units of the stock, Invest $$60\mathrm{.}98$ for one period at the rate r $=1\mathrm{.}025$

c$.$ Sell one put with a strike of $105,$ Short $0\mathrm{.}50$ units of the stock, Invest $$60\mathrm{.}98$ for one period at the rate r $=1\mathrm{.}025$

d$.$ Sell one put with a strike of $105,$ Buy $0\mathrm{.}50$ units of the stock, Borrow $$60\mathrm{.}98$ for one period at the rate r $=1\mathrm{.}025$