Consider an at-the-money European put option with a strike price of $30 and 6 months until expiration. The underlying stock does not pay dividends and has a historical volatility of 35%. The risk-free rate is 3%.

(5 points) What is the options delta?

(5 points) What is the value of the option?

(5 points) If the stock price immediately changed to $24, what would be the estimated

price of the option, using the delta approximation?

(5 points) Now consider the call option with the same information; compute its delta.

(5 points) If you purchase 10 of the put option and 5 of the call option, what is the delta of the resulting portfolio?

If the underlying stock in problem has a beta of 1.3, what is the beta of the put option?

(PLEASE NO EXCEL WORK.STEP BY STEP PROCESS WITH FORMULA)