The current price of a non-dividend-paying stock is $257 and the annual standard deviation of the rate of return on the stock is 41%. A European put option on the stock has a strike price of $250 and expires in 0.4 years. The risk-free rate is 2% (continuously compounded).

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

Now assume that the stock is expected to pay a dividend of $2.88 in 2 months.