The current price of a non$-$dividend$-$paying stock is $$53\mathrm{.}68$ and the annual standard deviation of the rate of return on the stock is $49\%.$

A hedge fund sold $4,600$ European call options on the stock. Each call has a strike price of $$50$ and expires in $0\mathrm{.}6$ years.

The risk$-$free rate is $3\%($continuously compounded$).$

What is the delta of the fund's position?

What is the gamma of the fund's position?

What is the vega of the fund's position, considering a one percentage point change in volatility?

What is the theta of the fund's position, considering one less calendar day to expiration?

What is the rho of the fund's position, considering a one percentage point change in the risk$-$free rate?