You have the following market data: PDQ stock price:102 Riskless interest rate (simple interest, i., the Annual Percentage Rate):00% Option...

13. You have the following market data: PDQ stock price:           102

Riskless interest rate (simple interest, i.e., the Annual Percentage Rate):  8.00% Option maturity: 3 months

Volatility: 0.30

Options are all European.

An option is for 1 share. Fractional shares and fractional options can be traded if you want to.

Options data:

Strike   Call price  Call delta  Call Gamma         Put price Put delta Put gamma

95          11                 .75            0.0208              2 1/2            -.25         0.0208

100           8                  .63            0.0247                4                -.37        0.0247

105           6                  .50            0.0261                8                -.50         0.0261

You are on the trading desk of a securities firm and you have just put on the following trade: Sold      100,000    95 strike PDQ puts

Bought  100,000  105 strike PDQ calls

a. What is the delta of this position?

b. What position do you have to take in PDQ stock in order to be delta neutral?

c. What is the gamma of your position?

d. Instead of trading the stock, you want to make a delta neutral position using the 100 strike calls. How many should you trade? What will be the gamma of that delta neutral position?

e. You want to use the stock and the 100 strike call to make your position both gamma neutral and delta neutral. How many 100 strike calls should you trade? What is the stock position you will need to make the whole position delta neutral?