有鑑於資產報酬常具有自我相關的特性，本文探討當標的資產報酬服從一階移動平均過程之選擇權（MA(1)-type option）評價。研究結果顯示，除了總變異因子（total volatility input）不同外，MA(1)-type option 的評價公式與 Black and Scholes 模型極為相似。而根據數值分析的結果，即使資產報酬間自我相關的程度薄弱，由一階移動平均過程產生之自我相關仍會對選擇權價值造成顯著影韾。 / This paper derives the closed-form formula for a European option on an asset with returns following a continuous-time type of first-order moving average process, which is named as an MA(1)-type option. The pricing formula of these options is similar to that of Black and Scholes except for the total volitility input. Specifically, the total volatility input of MA(1)-type options is the conditional standard deviation of continuous-compounded returns over the option's remaining life, whereas the total volatility input of Black and Scholes is indeed the diffusion coefficient of a geometric Brownian motion times the square root of an option's time to maturity. Based on the result of numerical analyses, the impact of autocorrelation induced by the MA(1)-type process is significant to option values even when the autocorrelation between asset returns is weak.

本文包含兩篇獨立文章，上篇內容為延後選擇型匯率連動權證，主要藉由風險中立評價法，以組合與拆解之觀念說明利用已知的權證類型，可以創造出更具效益之新奇權證，並對其評價與相關避險策略做進一步探討。下篇內容為重設型權證，重心在定期重設權證之風險特徵與策略應用，並以模擬一例證說明附加重設型權證之操作策略。

Quanto EIA是一種具有選擇權特性且能連結至外幣投資的保險年金商品.以往針對權益連動年金所做的文獻中,均未考慮Quanto的特性.本文利用風險中立評價法求算出六種具有Quanto特性的鎖高型權益連動年金商品的評價公式,並進一步利用數值分析來探討各個契約及市場參數對契約價值的影響. / Quanto Ratchet EIAs link to foreign investments and provide options-like properties. The literature covers the pricing of the EIAs that are not quantos. This paper intends to fill the hole. To derive the pricing formulas, we added an exchange rate model as well as a foreign risk-free rate model to the pricing framework of Black and Scholes. Our formulas cover quanto ratchet EIA products for both compound and simple versions that may have a return cap and employ two types of geometric return averaging. We further provide numerical analyses on how contract features and market parameters affect the contract value.

本研究利用美國芝加哥商品交易所針對 18 個城市發行之冷氣指數／暖氣指數衍生性商品與相對應之日均溫進行分析與評價。研究成果與貢獻如下：一、延伸 Alaton, Djehince, and Stillberg (2002) 模型，引入跳躍風險、隨機波動度、波動跳躍等因子，提出新模型以捕捉更多溫度指數之特徵。二、針對不同模型，分別利用最大概似法、期望最大演算法、粒子濾波演算法等進行參數估計。實證結果顯示新模型具有較好之配適能力。三、利用 Esscher 轉換將真實機率測度轉換至風險中立機率測度，並進一步利用　Feynman-Kac 方程式與傅立葉轉換求出溫度模型之機率分配。四、推導冷氣指數／暖氣指數期貨之半封閉評價公式，而冷氣指數／暖氣指數期貨之選擇權不存在封閉評價公式，則利用蒙地卡羅模擬進行評價。五、無論樣本內與樣本外之定價誤差，考慮隨機波動度型態之模型對於溫度衍生性商品皆具有較好之評價績效。六、實證指出溫度市場之市場風險價格為負，顯示投資人承受較高之溫度風險時會要求較高之風險溢酬。本研究可給予受溫度風險影響之產業，針對衍生性商品之評價與模型參數估計上提供較為精準、客觀與較有效率之工具。 / This study uses the daily average temperature index (DAT) and market price of the CDD/HDD derivatives for 18 cities from the CME group. There are some contributions in this study: (i) we extend the Alaton, Djehince, and Stillberg (2002)'s framework by introducing the jump risk, the stochastic volatility, and the jump in volatility. (ii) The model parameters are estimated by the MLE, the EM algorithm, and the PF algorithm. And, the complex model exists the better goodness-of-fit for the path of the temperature index. (iii) We employ the Esscher transform to change the probability measure and derive the probability density function of each model by the Feynman-Kac formula and the Fourier transform. (iv) The semi-closed form of the CDD/HDD futures pricing formula is derived, and we use the Monte-Carlo simulation to value the CDD/HDD futures options due to no closed-form solution. (v) Whatever in-sample and out-of-sample pricing performance, the type of the stochastic volatility performs the better fitting for the temperature derivatives. (vi) The market price of risk differs to zero significantly (most are negative), so the investors require the positive weather risk premium for the derivatives. The results in this study can provide the guide of fitting model and pricing derivatives to the weather-linked institutions in the future.