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1	緩長記憶效應下的選擇權評價彭貴田 Unknown Date (has links) 傳統效率市場假設股價的波動是隨機的，亦即股價是無法預測。近來的文獻指出股價的波動是不完全是隨機的，且股價的波動具有緩長記憶(long memory)的特性。在本文中我們以R/S分析發現臺灣股市的Hurst指數為0.68，即具有趨勢持續性(trend persistent)之效果，根據此依特性，我們根據Necula(2002)的研究，來評價台股選擇權，發現此新評價模式產生之價格較接近市場價格。緩長記憶碎形布朗運動 Hurst 指數 R/S分析碎形Black-Scholes選擇權評價
2	以厚尾分配及緩長記憶特性模型分析日圓匯率期貨報酬之風險值 / VaR Analysis for the Dollar/Yen Exchange Rate Futures Returns with Fat-Tails and Long Memory 鄭士緯, Cheng, Shih-Wei Unknown Date (has links) 本篇文章將採用長期記憶模型之一的HYGARCH模型，搭配1985年廣場協議後的日圓匯率期貨資料來估計日圓期貨匯率買入和放空部位的日報酬風險值，探討控管日圓匯率期貨在使用上的風險。為了更準確地計算風險值，本文採用常態分配、學生t分配以及偏態學生t分配來作模型估計以及風險值之計算。本文實證的結果將有兩方面的貢獻：首先，實證結果顯示當我們採用厚尾分配估計風險值時，樣本內風險值的估計誤差會與信賴水準的高低呈正比的現象，證明在極端的風險值估計上，厚尾分配均有較佳的表現。其次，與其他使用HYGARCH模型研究日圓匯率的文章相較，本文在風險控管層面上所提供的偏態學生t分配，於估計風險值時，比起只考慮厚尾的對稱學生t分配將來得更為有效，其不但在估計誤差上較小，而且根據Kupiec檢定法，其在樣本內的風險值估計也有較好的表現。此外，本文也將多方證明此資料的偏態分配屬於右偏。 / In order to manage the exposure of the dollar/yen futures returns with regarding the long memory behavior in volatility, we use the HYGARCH(1,d,1) model with the data after the Plaza Accord to compute daily Value-at-Risk (VaR) of long and short trading positions. To take into account the fat-tail situation in financial time series, we estimate the model under the normal, Student-t, and skewed Student-t distributions. The contribution of this article is twofold. First, the empirical results show that the bias of in-sample VaR increases as the confidence level increases when VaR is calculated with a fat-tail distribution. Second, we provide a better distribution, the skewed Student-t innovation, for estimating the HYGARCH model for the Japanese yen in respect of risk management because the bias under the skewed Student-t innovation is smaller than that under the Student-t distribution, and in-sample VaR of the models with a skewed Student-t distribution outperforms based on Kupiec test. In addition, we get the innovation skewed to the right through the in-sample VaR analysis. 長期記憶性(緩長記憶性) 雙曲自迴歸條件變異數風險值 Kupiec LR 檢定法日圓匯率期貨 Long Memory HYGARCH VaR (Value-at-Risk) Kupiec LR test the Dollar/Yen futures
3	Empirical Performance and Asset Pricing in Markov Jump Diffusion Models / 馬可夫跳躍擴散模型的實證與資產定價林士貴, Lin, Shih-Kuei Unknown Date (has links) 為了改進Black-Scholes模式的實證現象，許多其他的模型被建議有leptokurtic特性以及波動度聚集的現象。然而對於其他的模型分析的處理依然是一個問題。在本論文中，我們建議使用馬可夫跳躍擴散過程，不僅能整合leptokurtic與波動度微笑特性，而且能產生波動度聚集的與長記憶的現象。然後，我們應用Lucas的一般均衡架構計算選擇權價格，提供均衡下當跳躍的大小服從一些特別的分配時則選擇權價格的解析解。特別地，考慮當跳躍的大小服從兩個情況，破產與lognormal分配。當馬可夫跳躍擴散模型的馬可夫鏈有兩個狀態時，稱為轉換跳躍擴散模型，當跳躍的大小服從lognormal分配我們得到選擇權公式。使用轉換跳躍擴散模型選擇權公式，我們給定一些參數下研究公式的數值極限分析以及敏感度分析。 / To improve the empirical performance of the Black-Scholes model, many alternative models have been proposed to address the leptokurtic feature of the asset return distribution, and the effects of volatility clustering phenomenon. However, analytical tractability remains a problem for most of the alternative models. In this dissertation, we propose a Markov jump diffusion model, that can not only incorporate both the leptokurtic feature and volatility smile, but also present the economic features of volatility clustering and long memory. Next, we apply Lucas's general equilibrium framework to evaluate option price, and to provide analytical solutions of the equilibrium price for European call options when the jump size follows some specific distributions. In particular, two cases are considered, the defaultable one and the lognormal distribution. When the underlying Markov chain of the Markov jump diffusion model has two states, the so-called switch jump diffusion model, we write an explicit analytic formula under the jump size has a lognormal distribution. Numerical approximations of the option prices as well as sensitivity analysis are also given. 均衡分析歐式選擇權拉氏倒轉變換長記憶馬可夫跳躍擴散模型馬可夫控制瓦松過程數值倒轉方法換跳躍擴散過程變波動聚集波動度微笑 Equilibrium analysis European call option Laplace inverse transform Leptokurtic Long memory Markov jump diffusion model Markov modulated Poisson process Numerical inversion method Switch jump diffusion model Volatility clustering Volatility smile

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