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Investment Guarantees the new science phần 9

và năng động bảo hiểm rủi ro chiến lược cho câu hỏi: Đó là tốt hơn? Các đường cong CTE cho thấy rằng, trên trung bình (tức là, CTE0%), phương pháp tính toán bảo hiểm là hơn đáng kể lợi nhuận hơn so với phương pháp tiếp cận năng động-bảo hiểm rủi ro. Mặt khác, ở đuôi phải nguy cơ liên quan với phương pháp tiếp cận tính toán bảo hiểm lớn | 210 FORECAST UNCERTAINTY FIGURE 11.7 Estimated 95 percent CTE risk measure with and without control variate. The control variate method appears to work well with other distributions for the stock price and for other contract designs. The additional computation is small and the payoff with a good control variate is high. The more general form of the control variate method is to use E E Ecv - ECV 11.6 so that the variance of the estimate is V E V E e2V Ecv - 20Cov Ê ECV 11.7 The variance is minimized when the parameter ỊÌ is . r-r- Ó 1 Ịi- _ C V E ECV 11.8 V E CV In general we will not know ft to get the minimum variance estimator but some experimentation with different simulated pairs E ECV can provide an estimate using regression. For the GMAB example used in this section the parameter is around 1.0 so the estimate we have used is roughly optimal. The control variate method is straightforward to apply with little additional computation over ordinary simulation and as we have seen using a control variate provides dramatic improvements in accuracy in some cases. It works well for estimating the mean or the CTEs of the net present value of the liability for investment guarantees. The use of guarantee liabilities for estimating tail quantile measures has not achieved such good Variance Reduction 211 FIGURE 11.8 Estimated 95 percent quantile risk measure with CTE and quantile control variates and without control variate. results. The quantile estimate comes from a specific simulation value the one that happens to be in the correct place in the ordered sample and it is not clear what control variate might be useful. In Figure 11.8 the estimated 95 percent quantile for the 20-year GMAB is plotted with control variates again based on the rollover cost at time 10 years. The grey line indicates the estimate without variance reduction. The broken line uses the 95 percent quantile of the year 10 living benefit as a control variate and it does not improve accuracy .