Delta hedging, Greek letters
11.6. (20 points / 20 minutes) 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 Ivant 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