壽險準備金風險之衡量

ON THE WAY TO ESTIMATE THE RISK OF LIFE INSURANCE RESERVES

壽險準備金存續期間長之特性使得如何衡量準備金風險成為壽險公司首要之務。相較於傳統的P測度法與歐盟Solvency II之QIS 2所提出之Q測度法，本研究提出QPQ方法來衡量壽險準備金之風險。理論上，在P測度法下計算未來責任現值時，折現率須採用無風險利率加上風險溢酬，然而風險溢酬無客觀可行的方法來進行估計，因此，大部分精算文獻並未考量風險溢酬。在Q測度法下，是在風險中立假設下模擬市場風險因子未來可能的變化，無法描繪實際市場波動所造成準備金價值變動之風險。QPQ方法則可避免上述方法的缺點。在時點t=0時，以市場經濟狀態並在Q測度下計算最佳估計值來作為準備金之估計值。但在準備金風險衡量方面，壽險公司需先在P測度下模擬時點t=H之市場情境，再於每個模擬出來的市場情境所對應的Q測度下進行最佳估計，計算時點t=H下之準備金。重覆進行此步驟後可以得到時點t=H下準備金之分佈。再以對應於所關心的風險期間之無風險利率來折現，即可推得時點t=0下準備金之分佈。最後透過風險衡量值，如風險值或尾端風險期望值來衡量準備金之風險。本研究以生死合險、利變型年金與股票指數型基金為例進行模擬試算。數值結果發現P測度法與Q測度法所計算之準備金風險與QPQ方法的確有顯著差異。傳統P測度法可能會過度衡量風險，因其考量全段保障期間之風險。而Q測度下所計算之準備金風險低於QPQ方法所得之結果，顯示以Q測度法衡量準備金風險可能無法正確反映風險。由於準備金適足性對壽險公司清償能力有很大之影響，因此，基於保守監理考量，本研究建議壽險公司應採用QPQ方法來衡量準備金風險。

How to measure the risk of policy reserves is important for life insurers because policy reserves are the largest liabilities with long durations. In this paper, we propose the “QPQ” method for determining the risk of policy reserves. We compare our approach with the traditional P-measure approach and Q-measure approach proposed by QIS 2 of Solvency II. Under the P-measure approach, the discount rate should be theoretically adjusted by risk premiums. However, it is difficult to determine the risk premiums of liabilities, and thus most studies have not considered the risk premium adjustment. Under the Q-measure approach, risk factors are simulated under the assumptions of risk neutrality. The movements of the risk factors, however, do not reflect the real movements of risk factors, and thus can-not reflect the possible real-world fluctuation of the reserves. The QPQ method can avoid the drawbacks of the above approaches. Based on the QPQ method, life insurers use best estimate valuation to determine their reserves at time t = 0 under Q measure. Then they generate stochastic future economic states (risk factors) from time 0 to time T under P-measure and apply the best estimate valuation to quantify their reserves at time t = H. For each scenario of the simulated stochastic future economic states, the reserve is again computed using best estimate valuation. The distribution of the reserve at time t = H is then discounted back to time t = 0 by the risk-free rate with maturity H. At the last step, commonly used risk measures (e.g., VaR and CTE) on the reserve distribution at time t = 0 are used to quantify the risk margin of the reserves. We apply the QPQ method to calculate the risk of reserves of the endowment policy, interest sensitive annuity, and equity-indexed annuity. We find that there exist significant differences between the QPQ, P-measure, and Q-measure approaches. The risk of reserves is overestimated under P-measure. However, the risk margin under Q-measure is lower than that under the QPQ method, suggesting that the risk of reserves is underestimated under Q-measure. Since the adequacy of policy reserves is critical to the solvency of life insurers, we suggest life insurers adopt the QPQ method to estimate and manage the reserve risk.