The current price of a non$-$dividend$-$paying stock is $$52\mathrm{.}23$ and the annual standard deviation of the rate of return on the stock is $41\%.$ A European call option on the stock has a strike price of $$50$ and expires in $1$ years.

The risk$-$free rate is $5\%($continuously compounded$).$

Attempt $1/50$ for $10$ pts$.$

Part $1$

What is the price of the option?

$1+$ decimals

Attempt $20/50$ for $10$ pts$.$

Part $2$

What is the delta of the option?

$0\mathrm{.}65$

Correct $$

Delta of a call option:

$\backslash$Delta

$=$

$$

c

$$

S

$0$

$=$

N

$($

d

$1$

$)$

$=$

N

$($

$0\mathrm{.}433$

$)$

$=$

$0\mathrm{.}668$

As the stock price increase by $$1,$ the value of the option changes by $$0\mathrm{.}668.$

Attempt $1/50$ for $10$ pts$.$

Part $3$

What is the gamma of the option?

$4+$ decimals

Attempt $1/50$ for $10$ pts$.$

Part $4$

What is the vega of the option, considering a one percentage point change in volatility?

$3+$ decimals

Attempt $1/50$ for $10$ pts$.$

Part $5$

What is the theta of the option, considering one less calendar day to expiration?

$4+$ decimals

Attempt $1/50$ for $10$ pts$.$

Part $6$

What is the rho of the option, considering a one percentage point change in the risk$-$free rate?