Betty Lu, an option analyst at UMB Student Managed Fund analyzing European call and put options on the S&P 500.
The S&P 500 index closes at 2000. European call and put options on the S&P 500 index with the exercise prices shown below trade for the following prices:
| Exercise price | 1,950 | 1,975 | 2,000 | 2,025 | 2,050 |
| Call price | $ 88 | $ 66 | $ 47 | $ 33 | $ 21 |
| Put price | $ 25 | $ 26 | $ 32 | $ 44 | $ 58 |
All options mature in 88 days. The S&P 500 portfolio pays a continuous dividend yield of 1.56% per year and the annual yield on a Treasury Bill which matures on the same day as the options is 4.63% per year.
For Standard Dev – Annual: B7 to K7 use the below value:
| 12.88% | 11.25% | 10.09% | 9.66% | 9.07% | 13.22% | 11.09% | 10.01% | 9.91% | 9.69% |
Instructions:
Using the template provided:
Using the Black Scholes Option Pricing model, determine what is the implied volatility of each of these calls and puts for column A19 and A 25, respectively.
What pattern do these implied volatilities follow across exercise prices and between calls vs. puts?
Assignment 5-4
Betty Lu, an option analyst at UMB Student Managed Fund working on portfolio Diversification
There are two countries and all risky assets in both countries have a standard deviation of 45%. All pairs of risky assets within the same country have a local correlation coefficient of 30%, but all pairs of risky assets between countries have an international correlation coefficient of 10%. Consider an international diversification strategy of investing half of your money in an equally-weighted portfolio in country 1 and the other half in an equally weighted portfolio in country 2. As you increase the number of assets in your total portfolio, how much does this lower the risk of your portfolio?
Instructions:
Using the template provided determine how much does this lower the risk of the portfolio when Lu increase the number of assets in UMB total portfolio?
