A stock trades for $$$$44$ per share. A call option on that stock has a strike price of $$$$55$ and an expiration date six months in the future. When the volatility of the$$ stock's returns is$30\%,$ the Black and Scholes value of the option is$$ $$3\mathrm{.}82.$ Now$$ assume, the volatility of the$$ stock's returns is $55\%,$ and the$$ risk$-$free rate is $5\%.$ Intuitively, would you expect this to cause the call price to rise or$$ fall? By how much does the call price$$ change?

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Part $1$

$$Intuitively$,$ would you expect this to cause the call price to rise or$$ fall?$($Select the best answer$$ below.$)$

A$.$

The call price will rise with the volatility of the$$ stock's returns.

This is the correct answer.B$.$

The call price will fall with the volatility of the$$ stock's returns.

Your answer is not correct.C$.$

The call price will not change with the volatility of the$$ stock's returns.

Part $2$

The Black and Scholes value of this call option is $$$