The current price of a non-dividend-paying stock is $41 and the annual standard deviation of the rate of return on the stock is 40%.

A hedge fund sold 5,400 European call options on the stock. Each call has a strike price of $50 and expires in 0.3 years.

The risk-free rate is 4% (continuously compounded).

1) What is the price of a single call option?

2) What is the delta of the fund's position?

3) What is the gamma of the fund's position?

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

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

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