$1.$ Using the B S OPM Excel program calculate the call option price and put option price for each stock price shown below. Assume R $=2\mathrm{.}5\%,\backslash$sigma $=0\mathrm{.}50($variance $=\mathrm{.}25),$ t $=0\mathrm{.}25$ per year, X $=$ $$50,$ and no dividends.

S$0=30,35,40,45,50,55,60,65,70,75,$ and $80.$

a$.$ Paste $($Pic$)$ a picture of your Excel input output boxes.

b$.$ Comment on the ability of the B S OPM to capture the features of the call and stock price relations.

c$.$ Determine the call and put prices with a variability of $\backslash$sigma $=0\mathrm{.}60($Variance $=0\mathrm{.}36).$ Comment on the impact of changes in variability have on the B$-$S OPM values.

d$.$ Using the B$-$S OPM Excel program determine the values for the call and put Greeks when the stock is priced at $$50$: delta, Gamma, Theta, and, Vega. Define each of the Greeks.