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    題名: 馬可夫跳躍過程下美式選擇權之評價：黃金之實證分析
    其他題名: American Option Pricing under Markovian Jump Process: a Gold Price Empirical Analysis
    作者: 廖四郎
    貢獻者: 金融系
    日期: 2012
    上傳時間: 2016-04-12 16:06:51 (UTC+8)
    摘要: 本研究計畫針對美式選擇權的評價並以黃金美式選擇權進行實證分析，從過去黃金的報酬序列分析發現不同時期黃金價格產生的跳躍頻率也有所不同。文獻上Mills(2004)的觀察，發現黃金報酬率存在高狹峰與波動度具有長期的序列相關現象，若僅使用幾何布朗運動與Merton(1976)的跳躍擴散模型皆無法完全描述黃金報酬的特性。因此，本研究將採用Chang, et al. (2010)馬可夫狀態轉換跳躍擴散模型，來描述黃金價格的動態過程，此模型不僅能解釋報酬率為非對稱高狹峰、波動度微笑現象，亦能解釋長記憶與波動叢聚現象。利用EM演算法估計跳躍擴散模型及馬可夫狀態轉換跳躍擴散模型之參數，並以SEM演算法估計參數之共變異數矩陣。在評價理論的推導方面，Merton (1976)測度假設跳躍風險為非系統性且可分散的風險，而Gerber and Shiu (1994)採用的Esscher測度轉換允許跳躍風險為系統性且不可分散的風險，為考量跳躍風險是否可分散下有無風險溢酬，本計畫將利用Merton測度及Esscher測度轉換推導風險中立機率測度下金價之動態過程，再利用Longstaff 和Schwartz (2001)所提出的最小平方蒙地卡羅模擬進行美式黃金選擇權之評價。
    From the analysis of gold return, we find different jump rates of gold price appearing in corresponding periods. According to Mills (2004), there exists highly leptokurtic and long-run correlation in the return and volatility of the gold price respectively. However, the phenomena described above cannot be explained by the model of GBM and jump diffusion. Hence, we will adopt Markov modulated Poisson process model proposed by Chang, et al. (2010) to model the dynamics of the gold price. The advantage of using this model lies in its more perfectly characterizing the phenomena of leptokurtosis and volatility clustering existing in the return of the gold. Further, we use the EM and SEM algorithm to estimate the parameters of the model and the covariance matrix of the parameters respectively. Regarding the pricing methodology, the risk of jump is characterized as the diversifiable non-systematic risk under the assumption of Merton (1976); nevertheless, Gerber and Shiu (1994) took the risk of jump as undiversifiable systematic risk the and used Esscher tranfrom to take the risk premium of the jump into consideration. Accordingly, we use these two different methods to derive the dynamics of the gold price under risk-neutral measure and apply the least-squares Monte Carlo simulation proposed by Longstaff and schwartz(2001) to price the American options on the gold under the above two different risk-neutral measures.
    關聯: 計畫編號 NSC101-2410-H004-060
    資料類型: report
    顯示於類別:[金融學系] 國科會研究計畫

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