Suppose a European PUT option with strike price of $72 on a stock has 60 days until expiration (T = 60/365) and the stock pays zero dividend. Assume the current stock price So = $70, volatility o = 20%, and continuously compounded interest rate r = 0.06. Please keep four decimal points in the following calculation and use the d-N(d) table below. d -0.8956 -0.6240 -0.2663 -0.1852 0.1852 0.2663 0.6240 0.8956 N(d) | 0.1852 0.2663 0.3950 0.4265 0.5735 0.6050 0.7337 0.8148 a. (4 points) Use the Black-Scholes formula, what is the price of the put option? b. (4 points) How much is the delta of the put option? C. (6 points) Assume there is also a European call option with strike price of $65 on the same underlying asset. The call is currently selling at $6.0613 with delta being Page 6 of 7 0.8591. An investor is taking short positions in 3 call options and long positions in 2 put options described above. Use delta approximation to estimate the approximate portfolio value change if the stock price increases by $0.5. d. (6 points) Suppose a market maker delta hedge 100 written put position and after 1 day, the stock price changes to $72. How much is his hedged profit or loss? For this part, instead of going through the calculation using BS formula by yourself, make use of the results from above and the following numbers: BSPut(72, 72, 0.20, 0.06, 59/365, 0)= 1.9125 BSPutl(72, 72, 0.20, 0.06, 60/365, 0)= 1.9259 BSPutDelta(72, 72, 0.20, 0.06, 59/365, 0)= -0.4361 BSPutDelta(72, 72, 0.20, 0.06, 60/365, 0)= -0.4356