You bought 1,000 shares of a stock that does not pay any dividends and has a current price of $468. The annual standard deviation of continuously compounded returns on the stock is 34%, and the risk-free rate is 3.5% (continuously compounded).

A European put option on the stock has a strike price of $450 and expires in 0.75 years.

1) What should be the price (premium) of the put option?

2) How many put options should you trade to delta-hedge your portfolio? Enter a positive number for buying options, and a negative number for selling options.