本文採用LIBOR市場利率模型評價確定提撥制退休金計畫所附之收益率保證，此保證收益率連結至隨機LIBOR市場利率，在相關的文獻上(特別在隨機利率方面)，尚未有相關的研究。本文同時考慮兩種保證型態：到期日保證與多期保證，運用平賭過程理論，在延伸之LIBOR市場利率模型(ELMM)下推導此兩種保證的理論公式解。相較於其他利率模型或HJM模型，採用ELMM所推得之評價公式更適合於實務運用。為供實務運用，文中並探討如何進行參數校準，亦進行蒙地卡羅模擬以驗證模型理論解的準確性。 / We derive the pricing formulas for the guarantees embedded in defined contribution (DC) pension plans with the guaranteed minimum rate of return set relative to a LIBOR interest rate. The guaranteed rate associated with a stochastic LIBOR interest rate has not yet been studied in the relevant literature, particularly in the presence of stochastic interest rates. An extended LIBOR market model (LMM) is employed to price the interest rate guarantees embedded in DC pension plans under maturity and multi-period guarantees. The pricing formulas derived under the extended LMM are more tractable and feasible for practice than those derived under the instantaneous short rate models or the HJM model. Calibration procedures are also discussed for practical implementation. Monte Carlo simulation is provided to evaluate the accuracy of the theoretical results.

退休金是退休人未來生活的依靠，確保在退休後能得到適足的退休給付，政府在退休金上實施保證收益制度，此制度為最低保證利率與投資報酬率連結。本文探討退休金給付標準為確定提撥制，當退休金的投資報酬率是根據其連結之股價指數的表現來計算時，股價指數報酬率的模型假設為馬可夫調控跳躍過程模型，考慮市場狀態與布朗運動項、跳躍項的跳躍頻率相關，即為Elliot et al. (2007) 的模型特例。使用1999年至2012年的道瓊工業指數與S&P 500指數的股價指數對數報酬率作為研究資料，採用EM演算法估計參數及SEM演算法估計參數共變異數矩陣。透過概似比檢定說明馬可夫調控跳躍過程模型比狀態轉換模型、跳躍風險下狀態轉換模型更適合描述股價指數報酬率變動情形，也驗證馬可夫調控跳躍過程模型具有描述報酬率不對稱、高狹峰及波動叢聚的特性。最後，假設最低保證利率為固定下，利用Esscher轉換法計算不同模型下型I保證之確定提撥制退休金的評價公式，從公式中可看出受雇人提領的退休金價值可分為政府補助與個人帳戶擁有之退休金兩部分。以執行敏感度分析探討估計參數對於馬可夫調控跳躍過程模型評價公式的影響，而型II保證之確定提撥制退休金的價值則以蒙地卡羅法模擬並探討其敏感度分析結果。 / Pension plan make people a guarantee life in their retirement. In order to ensure the appropriate amount of pension plan, government guarantees associated with pension plan which ties minimum rate of return guarantees and underlying asset rate of return. In this paper, we discussed the pension plan with defined contribution (DC). When the return of asset is based on the stock indices, the return model was set on the assumption that markov-modulated jump diffusion model (MMJDM) could the Brownian motion term and jump rate be both related to market states. This model is the specific case of Elliot et al. (2007) offering. The sample observations is Dow-Jones industrial average and S&P 500 index from 1999 to 2012 by logarithm return of the stock indices. We estimated the parameters by the Expectation-Maximization (EM) algorithm and calculated the covariance matrix of the estimates by supplemented EM (SEM) algorithm. Through the likelihood ratio test (LRT), the data fitted the MMJDM better than other models. The empirical evidence indicated that the MMJDM could describe the asset return for asymmetric, leptokurtic, volatility clustering particularly. Finally, we derived different model's valuation formula for DC pension plan with type-I guarantee by Esscher transformation under rate of return guarantees is constant. From the formula, the value of the pension plan could divide into two segment: government supplement and employees deposit made pension to their personal bank account. And then, we done sensitivity analysis through the MMJDM valuation formula. We used Monte Carlo simulations to evaluate the valuation of DC pension plan with type-II guarantee and discussed it from sensitivity analysis.