Q2. You are interested in buying some put protection for SP500 ETF SPY. SPY trading at 470. You are interested in a PUT option with 25 delta (ie delta per PUT is -0.25). Annual sigma is $125. DTE is 20 days. Q2a. What is strike price that will generate that 25 delta for the put? (4 points) (hint: delta for put is connected to CDF function. Using delta, you can figure out 2-score that generates that delta. You can find the Z-score either using normal table or in EXEL with norm.s.inv() function. The input to that function is the cumulative probability and output is the Z-score. Then you can convert the Z-score to strike price). Q2b. You bought 50 put contracts with 25 delta. Market moved downward by $5 the next day. You did not hedge your put position. What is PnL from delta / gamma/ theta respectively? (4 points) (note: each contract corresponds to 100 shares). Q2c. Consider a market marker who sold those 50 puts to you. He immediately hedged the position delta with underlying shares. How many shares does he need to sell immediate? (4 points) Page 3 Q2. You are interested in buying some put protection for SP500 ETF SPY. SPY trading at 470. You are interested in a PUT option with 25 delta (ie delta per PUT is -0.25). Annual sigma is $125. DTE is 20 days. Q2a. What is strike price that will generate that 25 delta for the put? (4 points) (hint: delta for put is connected to CDF function. Using delta, you can figure out 2-score that generates that delta. You can find the Z-score either using normal table or in EXEL with norm.s.inv() function. The input to that function is the cumulative probability and output is the Z-score. Then you can convert the Z-score to strike price). Q2b. You bought 50 put contracts with 25 delta. Market moved downward by $5 the next day. You did not hedge your put position. What is PnL from delta / gamma/ theta respectively? (4 points) (note: each contract corresponds to 100 shares). Q2c. Consider a market marker who sold those 50 puts to you. He immediately hedged the position delta with underlying shares. How many shares does he need to sell immediate? (4 points) Page 3
