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    Title: 匯率選擇權隱含波動率與即期匯率之非線性關係
    Other Titles: The nonlinear relationship between the spot foreign exchange rate and the implied volatility
    Authors: 陳彥錞;Chen, Yan-chun
    Contributors: 淡江大學財務金融學系碩士在職專班
    聶建中;Neih, Chien-chung
    Keywords: 歷史波動率;隱含波動率;風險偏向;蝶式價差;門檻誤差修正模型;Historical volatility;Implied Volatility;Risk Reversal;Butterfly;Threshold Error Correction model
    Date: 2006
    Issue Date: 2010-01-11 00:49:57 (UTC+8)
    Abstract: 在現代財務理論及實務中,無論是衡量風險值(Value at Risk)亦或衍生性商品評價,波動率的衡量及估計皆為主要之關鍵課題。依據對未來隱含波動率之走勢研判,交易商可建立選擇權波動率部位,再根據敏感度分析及預期未來標的資產走勢,以標的資產或選擇權做動態避險,而使其部位損益變化僅受隱含波動率變動之影響。因此,標的資產價格與隱含波動率間以及歷史波動率與隱含波動率間之相互關係探討,有助於交易商對其波動率部位做有效管理。
    過去文獻有關探討標的資產價格與隱含波動率之關係,大多偏重於權益選擇權,相對以匯率選擇權探討之比例較少。本文以門檻自我回歸模型及門檻誤差修正模型,探討歐元兌美元匯率選擇權波動率市場中之主要交易標的:價平隱含波動率(ATM Implied Volatility)、25D風險偏向(Risk Reversal)及25D蝶式價差(Butterfly)與即期匯率間之非線性關係,以及經由不同方式產生之歷史波動率與價平隱含波動率間之非線性關係。以提供交易商在建立選擇權波動率部位及進行部位避險或短期投機性交易時,除傳統基本面、技術面分析及主觀之趨勢判斷外之另一參考資訊。並經由不同交易標的之long或short,以產生利潤。
    實證結果顯示:一、以非線性KSS法及線性KPSS法進行單根檢定,發現所有變數資料之整合級次均為1,即為I(1)序列。二、以門檻自我回歸模型檢定包括即期匯率與ATM隱含波動率、即期匯率與25D Risk Reversal、即期匯率與25D Butterfly、ATM隱含波動率與GARCH歷史波動率以及ATM隱含波動率與簡單移動平均歷史波動率等,各組變數間之長期均衡均具有非線性門檻共整合關係。三、以門檻誤差修正模型為基礎,探討各組研究變數間之長、短期互動關係及往長期均衡調整過程,發現皆各有不一致之特定關係。例如當即期匯率正向變動時,考慮其短期互動關係,則可建立Short ATM Volatility及Long 25D Risk Reversal之選擇權交易部位,進而使Volatility Smile產生變動,產生與Hull and White(1987)相近之結果。
    The measure and estimate of volatility are the key topics in pricing derivatives or value at risk. According to the view of the trend in volatility, traders can make the option portfolio value only depend on future volatility move by hedging process. Hence the research of the relationship between the price of underlying asset and the implied volatility can help traders to manage option portfolio.
    The empirical literatures in past about the relationship most focused on equity option. This paper discusses for the EUR/USD spot FX rate, historical volatility the ATM implied volatility, 25D risk reversal, and 25D butterfly in the FX option market employing a non-linear version based on asymmetric threshold autoregressive model and threshold error correction model.
    The results suggest the significant asymmetric cointegration in spot and ATM implied volatility, spot and 25D risk reversal, spot and 25D butterfly, ATM implied volatility and GARCH volatility, ATM implied volatility and simple moving average volatility. Furthermore, the results from Granger-Causality tests based on corresponding threshold error-correction model clearly point out the asymmetric causality in the short run and asymmetric price transmissions between these pairs in the long run. When the spot moved positively, considering short-term causality, trader can short ATM implied volatility and long 25D risk reversal to ride the volatility smile. Hence the curve will shift and correspond to the result of Hull and White (1987).
    Appears in Collections:[財務金融學系暨研究所] 學位論文

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