本研究的目的為使用雙指數跳躍模型(DEJM)來評價確定提撥制退休金計畫所 附之利率保證(IRGEIDCPs)。DEJM 考慮了asymmetric leptokurtic 與volatility smile 的實證現象並且可以納入投資人對市場各種好壞消息的情緒反應。因此，使用DEJM 評價IRGEIDCPs 預期將比一般只有使用布朗運動(geometric Brownian motion; GBM) 的模型來得更為準確。DEJM 對許多不同的選擇權均可獲得評價公式，所以我們預 期將可推導出IRGEIDCPs 在DEJM 架構下的評價公式。 文中將會分析比較在 DEJM 與GBM 架構下之評價差異。為能供實務運用，並 將探討如何進行參數校準(Calibration)；文中亦將進行蒙地卡羅模擬（Monte Carlo Simulation）以驗證模型理論解的準確性與效率性。最後亦將進行情境分析(scenario analysis)以探討重要跳躍參數(jump parameters)如何影響IRGEIDCPs 的評價，並且提 供如何實行風險管理的準則。 This research plan attempts to derive the pricing formulas for the interest rate guarantees embedded in defined contribution pension plans (IRGEIDCPs) under a Double Exponential Jump-Diffusion Model (DEJM). DEJM incorporates two empirical phenomena- the asymmetric leptokurtic features and the “volatility smile” - and investors’ sentiment toward various good or bad news. As a result, pricing IRGEIDCPs under DEJM should be more precise than under a simple geometric Brownian motion (GBM) model. DEJM can produce analytical solutions for a variety of option pricing problems so that the IRGEIDCPs pricing formulas are expected to be derived under DEJM. The difference between pricing IRGEIDCPs under DEJM and under a simple GBM will be analyzed. Calibration procedures will also be discussed in details for practical implementation. In addition, Monte-Carlo simulation will be provided to evaluate the accuracy and efficiency of the theoretical formulas. Scenario analysis will be carried out to discuss that how the primary jump parameters affect the prices of IRGEIDCPs and guides to risk management will also be provided.
