Q3.(40 marks) You own 1000 stocks of Amazon's stock. The current stock price is 1750. You believe that the stock price will double in two years, but you believe that the stock price will drop in the next six months. Therefore, based on your expectations, you want to benefit from the stock price movement by writing options. The options available in the CBOE are as follows Option Type Call Call Call Put Strike Price $1,720 $1,730 $1,750 $1,720 $1,730 $1,750 Maturity 3 Months 3 Months 3 Months 3 Months 3 Months 3 Months Put Put a. What is the name of the strategy you will create that includes both the stocks you own and the options you will write? Which option you will choose and why? (5 marks) b. The price of a call option on Amazon's stock that expires in 9 months with a strike price $1.720 is $103.15. If the 9-month Treasury bill is 2.315% (APR rate), what is the implied volatility? (10 marks) c. Using the implied volatility in the previous question, and based on the Black-Scholes-Merton model, what is the expected income from this strategy you chose in part (a)? (20 marks) d. You change your mind and decided to hold a riskless portfolio of the options you shorted and the stock you own. How many stocks you have to buy or sell to adjust your holding of Amazon to form a riskless portfolio? (10 marks) Q3.(40 marks) You own 1000 stocks of Amazon's stock. The current stock price is 1750. You believe that the stock price will double in two years, but you believe that the stock price will drop in the next six months. Therefore, based on your expectations, you want to benefit from the stock price movement by writing options. The options available in the CBOE are as follows Option Type Call Call Call Put Strike Price $1,720 $1,730 $1,750 $1,720 $1,730 $1,750 Maturity 3 Months 3 Months 3 Months 3 Months 3 Months 3 Months Put Put a. What is the name of the strategy you will create that includes both the stocks you own and the options you will write? Which option you will choose and why? (5 marks) b. The price of a call option on Amazon's stock that expires in 9 months with a strike price $1.720 is $103.15. If the 9-month Treasury bill is 2.315% (APR rate), what is the implied volatility? (10 marks) c. Using the implied volatility in the previous question, and based on the Black-Scholes-Merton model, what is the expected income from this strategy you chose in part (a)? (20 marks) d. You change your mind and decided to hold a riskless portfolio of the options you shorted and the stock you own. How many stocks you have to buy or sell to adjust your holding of Amazon to form a riskless portfolio? (10 marks)
