All assumptions of the Black$-$Scholes$-$Merton option pricing model hold. Stock XYZ is priced at $S_{xYZ}=$$$50.$ It has volatility

$=25\%$ per year. The annualized continuously$-$compounded risk$-$free interest rate is $r=4\mathrm{.}3\%.$

Compute the price of a European call option with strike price $K=$$$50,$ which matures in $9$ months.

$5\mathrm{.}082$

Compute the option Delta at time $t=0.$

$0\mathrm{.}601$

Suppose that at time $t=0$ the stock price changes instantaneously from $S_{xYZ}=50$ to $S_{xYZ}=53.$ Compute the

resulting change in the option price.

$

Suppose that at time $t=0$ the stock price changes instantaneously from $S_{xYZ}=50$ to $S_{xYZ}=53.$ Compute the

resulting change in the value of the replicating portfolio for this option.

$1\mathrm{.}804$

Suppose that at time $t=0$ the stock price changes instantaneously from $S_{xYZ}=50$ to $S_{xYZ}=47.$ Compute the

resulting change in the option price.

$

Suppose that at time $t=0$ the stock price changes instantaneously from $S_{xYZ}=50$ to $S_{xYZ}=47.$ Compute the

resulting change in the value of the replicating portfolio for this option.