本研究的目的為使用馬可夫調整跳躍擴散模型(Markov-modulated jump-diffusion model; MMJDM)來評價財務契約中所附之相對報酬率保證之價值 (RGEIFCs) 。MMJDM 中同時考慮了rare events 與 time-inhomogeneity 對評價的影 響。因此，使用MMJDM 評價RGEIFCs 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。 文中將會分析比較在 MMJDM 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)以探討重要參數如何影響RGEIFCs 的評價，並且提供如何實行風險管理的 方針。 This research plan attempts to derive the pricing formulas for the relative guarantees embedded in financial contracts (RGEIFCs) under a Markov-modulated jump-diffusion model (MMJDM). Both rare events and time-inhomogeneity in the real market are incorporated in MMJDM simultaneously. As a result, pricing RGEIFCs under MMJDM should be more precise than under a simple geometric Brownian motion (GBM) model. The difference between pricing RGEIFCs under MMJDM 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 parameters affect the prices of I RGEIFCs and guides to risk management will also be provided.
