附保證投資型保單提供額外保證給予保戶，而對於保險公司來說保證的部分可能會承擔財物損失，因此在評價方式相當重要。為了避免可能發生的財務問題，保險公司應要了解相關避險工具的使用與方法。本研究探討避險策略對附保證投資之影響，由於許多因素會影響到建構避險策略，如保戶死亡率、保證利率、到期日等Hardy (2003)。本研究以二項樹(Binomial tree)方法模擬各附保證商品之避險，例如最低滿期給付(guaranteed minimum maturity benefit ; GMMB)、最低死亡給付(guaranteed minimum death benefit ; GMDB)及最低保證提領(guaranteed minimum withdrawal benefit ; GMWB)等，建構避險方式以Hardy (2003)將商品評價拆解為無風險部位與風險部位，並以delta避險策略來觀察各保證商品避險效率，並且與Black-Scholes方法比較。對於其他附保證商品而言以二項樹評價跟Black-Scholes評價其避險效率差不多。另一方面對於GMWB商品來說，以5年期與10年期皆為保本型的GMWB相比，以5年期保單避險效率效果較好，原因在於存續時間較長而增加長年期保單的不確定性。而改變避險頻率來看，月頻率與季頻率無太大差別，而在半年頻率來說，損失補回的能力項較於前兩者來說相對薄弱。而考量交易成本角度，對於GMWB商品來說並無太大的差別。顯示不同影響評價的因子對於避險結果來說也會產生不同變化的影響。

Investment guarantee insurances provide the insured additional guarantee for protection, but these guarantees may bring a tremendous loss for insurance company. Therefore, the construction of valuation for guarantee product is very important. To avoid this loss from guarantee, hedging strategy and instrument should be considered prudentially. Many factors affect the valuation structure such as mortality, guarantee rate, maturity. Therefore, taking some factors in consideration for valuation, we use Black-Scholes formula and binomial tree method to simulate different investment guarantees and simulate guaranteed minimum withdrawal benefit (GMWB) by tree method that GMWB could not be simulated by Black-Scholes formula. For construction of hedging, we follow Hardy (2003) to separate two parts, risk-free component and risky component, and use delta hedging to observe the effectiveness of delta hedging for different investment guarantee. For our observation, there are no significant different to investment guarantee in delta hedging by different two valuation methods. However, for GMWB, the maturity at 5 years is more effective than at 10 years. The reason is that the longer duration makes more uncertainty for hedging. In frequency of hedging for GMWB, there is no significant different between monthly and quarterly, but when frequency is half of year, the effectiveness is less powerful. Moreover, there is almost same effective in different transaction cost. These indicates that different factors affect hedging to different effects.

1. Coleman, T. F., Y. LI, and M. C. Patron (2006): Hedging Guarantees in Variable Annuities under Both Equity and Interest Rate Risks, Insurance: Math. Econ. 38(2), 215–228.
2. Cox, J. C., Ross, S.A. and Rubinstein, M. (1979). Options pricing: a simplified approach. Journal of Financial Economics 7, 229–63.
3. Dickson, D., M. Hardy, and H. Waters. (2009), Actuarial Mathematics for Life Contingent Risks. International Series on Actuarial Science (Cambridge, UK: Cambridge University Press).
4. Feng, R., Volkmer, H.W., (2012). Analytical calculation of risk measures for variable annuity guaranteed benefits. Insurance Math. Econom. 51 (4), 636–648.
5. Hardy, M. R. (2003): Investment Guarantees Modeling and Risk Management for Equity-Linked Life Insurance, John Wiley＆Sons.
6. Hull, J. C. (2015). Options, Futures and Other Derivatives, 9th edition. Upper Saddle River: Prentice Hall.
7. Klebaner, F.C. (1998), Introduction to Stochastic Calculus with Applications (Imperial College Press, London).
8. Kolkiewicz, A., Liu, Y., (2012). Semi-static hedging for gmwb in variable annuities. North American Actuarial Journal 16 (1), 112–140.
9. Liu Y. (2010). Pricing and Hedging the Guaranteed Minimum Withdrawal Benefits in Variable Annuities. Electronic Theses and Dissertation, University of Waterloo
10. Milevsky, M.A. & Salisbury, T.S. (2006): Financial valuation of guaranteed minimum withdrawal benefits, Insurance: Mathematics and Economics 38(1), 21–38.
11. Piscopo, G. & Haberman, S. (2011). The valuation of guaranteed lifelong withdrawal benefit options in variable annuity contracts and the impact of mortality risk. North American Actuarial Journal, 15(1), pp. 59-76.
12. T. F. Coleman, Y. Kim, Y. Li and M. Patron. (2007). Robustly Hedging Variable Annuities with Guarantees under Jumps and Volatility Risks. The Journal of Risk and Insurance, Vol. 74, No. 2 (Jun., 2007), pp. 347-376
13. TianShyr Dai, Sharon S. Yang and Liang‑Chih Liu (2015), Pricing Guaranteed Minimum/Lifetime Withdrawal Benefits with Various Provisions under Investment, Interest Rate and Mortality Risks, Insurance Mathematics and Economics, 64:364:379.
14. Yang, S.S., Dai, T.-S., (2013). A flexible tree for evaluating guaranteed minimum withdrawal benefits under deferred life annuity contracts with various provisions. Insurance Math. Econom. 52 (2), 231–242.
15. 黃克崴(2008)，隨機投資模型在精算上的應用，東吳大學財務工程與精算數學研究所碩士論文。
16. 謝昌宏(2011)，在Hull-White隨機利率及動態生存率下評價保證最低提領給附保險附約，國立交通大學資訊管理研究所碩士論文
17. 詹惟淳(2013)，考慮保戶行為下對附保證投資型商品準備金之評估，國立中央大學財務金融研究所碩士論文