Question 4 i. Do you agree with the statement "The implied volatility of an option which has a given strike price and expiry date can vary over time"? Explain in detail. [5 marks] H. A bond has face value $100 and it is priced at par. Its yield-to-maturity is 7% and its duration is 7.51 years. Next, the bond price changes to $95.23 and the new yield-to- maturity is 7.70%. How well does duration capture interest rate risk? IL Consider three randomly generated variables Z, Z, and Z. Explain what the following two figures below show. -4.0000 Scatter Plot of Z1 vs 23 4.0000 5.0000 2.0000 10000 boo 428000000 ** Boo -4.0000 4.0000 [5 marks] Frequencies: 21, 22, 23 [5 marks] iv. A 65-year-old pensioner wants to invest 500,000 for the next 5 years. She is considering investing in an investment strategy in which she would invest 20% of her assets in a risk-free bond with 5% continuously compounded annual interest and the remaining 80% in a risky asset with 8 % mean return and 18% standard deviation. The pensioner applied Monte Carlo simulation to decide whether she should invest her money in this investment strategy. The Excel spreadsheet below reports the end- of-year wealth based on one simulation that she conducted. Write down and explain the Excel formula used to calculate the values in cells E12 and F12, in the Excel spreadsheet below: Question 4 i. Do you agree with the statement "The implied volatility of an option which has a given strike price and expiry date can vary over time"? Explain in detail. [5 marks] H. A bond has face value $100 and it is priced at par. Its yield-to-maturity is 7% and its duration is 7.51 years. Next, the bond price changes to $95.23 and the new yield-to- maturity is 7.70%. How well does duration capture interest rate risk? IL Consider three randomly generated variables Z, Z, and Z. Explain what the following two figures below show. -4.0000 Scatter Plot of Z1 vs 23 4.0000 5.0000 2.0000 10000 boo 428000000 ** Boo -4.0000 4.0000 [5 marks] Frequencies: 21, 22, 23 [5 marks] iv. A 65-year-old pensioner wants to invest 500,000 for the next 5 years. She is considering investing in an investment strategy in which she would invest 20% of her assets in a risk-free bond with 5% continuously compounded annual interest and the remaining 80% in a risky asset with 8 % mean return and 18% standard deviation. The pensioner applied Monte Carlo simulation to decide whether she should invest her money in this investment strategy. The Excel spreadsheet below reports the end- of-year wealth based on one simulation that she conducted. Write down and explain the Excel formula used to calculate the values in cells E12 and F12, in the Excel spreadsheet below: