Help me crack the following questions.
(/4 points) You are an actuary working in the Investment Department at JDY Life. JDY Life plans to offer a new indexed annuity product and is considering linking it to a composite index created by combining the ABC Fund and the XYZ Fund Your manager, Maggie, has asked for your assistance with understanding the correlation between the two funds for capital budgeting purposes and how it may change over time. Maggie has selected these two funds as she believes there may exist a natural hedge. She would ultimately like to model the joint distribution of the composite index using a copula and seeks an appropriate parameterization. Maggie has provided you with the following information regarding the daily price change for each index over the past 30 days. ABC XYZ Time (t) j k Rank of Rank of Fund (j.) Fund (k) 30 -3.83% -1.36% 0.052% 28 23 -29 2.55% 0.14% 0.004% 1 15 -28 2.11% 1.15% 0.024% 4 5 -3 -0.68%% 0.64%% -0.004% 20 11 0.50% 0.02% 0.000% 15 16 -0.99% -0.19%% 0.002% 18 Arithmetic Mean -0.109% -0.155% 0.006% 15.50 15.50 Variance 0_034% 0.021% 0.001% 74.92 74.92 Covariance 18.45 (a) (3 points) In order to calibrate a copula for modeling the joint distribution of the two funds, you first must determine an appropriate correlation metric. You consider the following correlation coefficients: . Pearson's rho Spearman's rho Kendall tau Additional analysis shows that there are 253 concordant pairs of index returns in the dataset. (i) Calculate each correlation metric based on the data provided. Show all work. (ii) Describe the advantages and disadvantages of each metric that you should consider when selecting an appropriate correlation metric for parameterizing a copula.(b) (5 points) The first step in forecasting correlation between the two funds is to forecast the volatility of the individual funds. In order to forecast the volatility of each fund's value, you fit a GARCH(1,1) model, as shown below, to each series of fund returns: h, =a +ar_+ ph,_ The parameters for each model are provided in the following table: Parameter Fund ABC Fund XYZ 0.0001 1.0002 0.1610 0.2570 B 0.7770 0.5650 You are also given the initial observation of each of the funds: Time (t) Fund ABC j Fund XYZ k 5.01% 4.89% (i) Determine which fund has the higher expected variance. Show all work. (ii) Assume that the to conditional variances for each fund are equal to the empirical variances shown in the table on the previous page. Calculate the conditional variances for the next two time steps, (=1 and t=2 for each fund using the GARCH(1,1) model. Show all work. (iii) Maggie explains that there are simple modifications that can be made to the basic GARCH(1,1) model in order to more accurately reflect the behavior of typical financial time series. Explain why the following modifications may be implemented for volatility forecasting: Using the absolute value of the innovation term Using a separate parameter for positive shocks and negative shocks(c) (3 points) Maggie believes that the RiskMetrics approach is more appropriate than the GARCH model for forecasting the covariance between the two funds. She suggests using a risk decay factor of 0.95 and the empirical covariance as the t=0 conditional covariance. The formula for forecasting the covariance using the RiskMetrics approach is given below. (i) Identify two arguments in favor of using the RiskMetrics approach for forecasting covariance. (ii) Calculate the forecasted =1 Pearson correlation coefficient using the Risk Metrics approach and the results of part (b)(ii). Show all work. (d) (3 points) Based on the results of your analysis, your team plans to implement the forecasting model to assess short-term capital adequacy for the annuity block. (i) Explain how model risk could arise while calibrating and implementing the models described above. (ii) Recommend three model validation best practices that could be incorporated to help manage and mitigate model risk. Justify your response
