自從Black-Scholes (1973) 選擇權定價模型發表之後，文獻上已經發展出許多衍生性商品定價的模型，在Black-Scholes模型中，假設標的資產的現貨價格為幾何布朗運動，可是越來越多的證據顯示，這些標的資產的現貨價格不一定符合幾何布朗運動，所以後來許多的學者對這些假設慢慢地加以修正，最著名的有Merton (1976) 的跳躍模型(Jump diffusion)，Heston (1993) 隨機波動模型(Stochastic volatility model)和 Bates (1996) 隨機波動跳躍擴散模型(Stochastic volatility jump diffusion model) 。在溫室效應日趨嚴重的今日，碳衍生性商品提供降低碳排放的市場機制越來越重要。所以本文的目的即在研究碳衍生性商品的定價， Daskalakis, Psychoyios和Markellos (2009) 發現碳衍生性商品的定價中使用跳躍擴散模型會比Black - Scholes模型績效還要好。由於碳現貨價格的變異數不一定是常數，所以若碳現貨價格的變異數是隨機的，則使用隨機波動模型，應該會對碳衍生性商品的價格有較佳的解釋能力。

本文使用無母數檢定，驗證碳現貨價格的變異數確實是隨機的，因此本文使用了隨機波動模型與隨機波動跳躍擴散模型來研究碳衍生性商品的定價。然而本文的研究標的“碳”即是所謂的歐盟許可(European Union Allowances)，1單位的歐盟許可等於1公噸的二氧化碳排碳權。我們將樣本資料分為三階段，第一階段是歐盟許可交易的政策改變前，第二階段是歐盟許可交易的政策改變後，第三階段則是歐盟許可重新被允許開始交易。我們使用最大概似估計法來估計Black-Scholes模型與跳躍擴散模型，而隨機波動模型與隨機波動跳躍模型，我們則使用狀態空間模型(state-space models) 與Kalman Filter來估計。然後依據估計的模型使用蒙地卡羅模擬來計算碳衍生性商品的價格。最後我們發現到在碳期貨價格用跳躍擴散模型和隨機波動跳躍擴散模型顯著優於其他的模型，而在碳選擇權價格部分隨機波動跳躍擴散模型分析則顯著地比其他模型還要好。

In basic Black-Scholes model, the price of underlying assets of financial derivatives such as stock prices, interest rates and foreign exchange rates are originally assumed to follow a diffusion process. However increasing empirical evidence show that Geometric Brownian motion are not appropriate in modeling the price of these financial assets. So, many successive literatures develop other types of pricing models of financial derivatives. Merton (1976) proposed jump diffusion model, Heston (1993) developed stochastic volatility model and Bates (1996) suggested stochastic volatility jump diffusion models. Due to the greenhouse effect, Carbon derivatives which can help us to reduce the emission of carbon are very important, so the target of this paper focused on the pricing issues of carbon derivatives. Daskalakis, Psychoyios, and Markellos (2009) apply jump diffusion process to model the carbon spot price and compare the performance of Black-Scholes models and jump diffusion model in pricing carbon derivatives. In fact, the variance of carbon spot price may not be a constant. So if the variance of carbon spot price is indeed stochastic, the adoption of stochastic volatility model should have better prediction performance.

In this paper we apply nonparametric method to substantiate that the variance of carbon spot price is stochastic. So we use stochastic volatility model and stochastic volatility jump diffusion model to analyze the pricing of carbon derivatives. In this paper so called “carbon”is actually European Union Allowances. 1 unit of EUA is equal to 1 ton of permission carbon emission. We divided sample period into three phrases, the first phase was that the policy which was relevant to the trade of EUA change before 2006 April, the second phase was that the policy which was relevant to the trade change after 2006 April and the third phase was that the European Union Allowances is allowed to restart trading on 26/02/2008. We use the maximum likelihood method to estimate the Black-Scholes model and the jump diffusion model, but for the stochastic volatility model and stochastic volatility jump model we use the state space model and the Kalman Filter to estimate. Then based on estimated models we use estimates of the Monte Carlo simulation to estimate the prices of the carbon derivative. Finally, we find that the stochastic volatility jump diffusion model which has both spot price with jump and volatility with jump have significant outperformance in pricing carbon derivatives.

摘要 I
Abstract II
目錄 III
表目錄 IV
圖目錄 V
第一章 緒論 1
第二章 碳衍生性商品文獻回顧 3
第三章 相關的衍生性商品定價模型 5
第一節 Black-Scholes 模型(BS) 5
第二節 跳躍擴散模型(Jump diffusion, JD) 6
第三節 隨機波動模型(Stochastic Volatility, SV) 7
第四節 隨機波動跳躍模型(Stochastic Volatility Jump Diffusion Models) 8
第五節 碳的隨機波動跳躍擴散模型 9
第四章 碳衍生性商品定價模型的估計與模擬 10
第一節 碳衍生性商品現貨價格與現貨價格波動的估計 10
第二節 碳衍生性商品價格的蒙地卡羅(Monte Carlo)模擬 13
第五章 實證結果 14
第一節 資料 14
第二節 碳(EUA)現貨價格的模型 21
第三節 碳衍生性商品期貨合約的定價 23
第四節 碳衍生性商品選擇權的定價 25
第六章 結論 30
參考文獻 30

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