$(10$ points$)$ Using the Black$/$Scholes Option Pricing Model, calculate the value of the call option given:

$S=70$;

$x=80$;

$T=3$ months;

${}^2=49$;

$R_f=10\%$

$(3(3$ points$)$ What is the intrinsic value of the call?

$(3)(2$ points$)$ What stock price is necessary to break$-$even?

$(4.(3$ points$)$ If volatility were to increase, the value of the call would

$(2$ points$)$ If the exercise price would increase, the value of the call would

$(2$ points$)$ If the time to maturity were $6-$months, the value of the call would

$(2$ points$)$ If the stock price were $$62,$ the value of the call would

$(3$ points$)$ What is the maximum value that a call can take? Why?

$(3$ points$)$ Explain which option $($i$.$e$.$ put or call$)$ positions $($i$.$e$.$ long or short$)$ offers the most risk.