The current price of Kinston Corporation stock is $$10.$ In each of the next two years, this stock price can either go up by $$3$ or go down by $$2.$ Kinston stock pays no dividends. The one year risk$-$free interest rate is $5\%$ and will remain constant. Using the binomial pricing model, claculate the value of a two$-$year at$-$the$-$money call option on Kinston stock.

a$.$ What is the value of call option at year $1$ if the stock price goes up$?$ Mark the correct answer.

$$4\mathrm{.}23$

$$4\mathrm{.}83$

$$4\mathrm{.}63$

$$5\mathrm{.}03$

$$3\mathrm{.}48vv$ OK

Mark $1\mathrm{.}0$ out of $1\mathrm{.}0$

The correct answer is:

$$3\mathrm{.}48$

b$.$ What is the value of call option at year $1$ if the stock price goes down? Mark the correct answer.

$$1\mathrm{.}06$

$$0\mathrm{.}66$

$$0\mathrm{.}86$

$$1\mathrm{.}26$

$$0\mathrm{.}46$ OK

Mark $1\mathrm{.}0$ out of $1\mathrm{.}0$

The correct answer is:

$$0\mathrm{.}46$

c$.$ What is the value of call option at year $0?$ Mark the correct answer.

$$2\mathrm{.}34$

$$2\mathrm{.}74$

$$2\mathrm{.}94$

$$1\mathrm{.}87OK$

$$2\mathrm{.}14$

Mark $1\mathrm{.}0$ out of $1\mathrm{.}0$

The correct answer is:

$$1\mathrm{.}87$