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).

目    錄
第一章  緒論…………………………………………	1
第一節  研究動機……………………………………	1
第二節  研究目的……………………………………	3
第三節  研究架構……………………………………	3
第二章  理論與文獻探討 ……………………………	5
第一節  歷史波動率…………………………………	5
第二節  隱含波動率…………………………………	9
第三節  匯率選擇權隱含波動率市場………………	13
第三章  研究方法……………………………………	27
第一節  單根檢定……………………………………	27
第二節  GARCH模型估計及檢定……………………	29
第三節  門檻自我迴歸模型及門檻共整合檢定……	29
第四節  門檻誤差修正模型…………………………	31
第四章  實證結果……………………………………	33
第一節  資料蒐集及處理……………………………	33
第二節  日報酬率GARCH模型估計及檢定…………	35
第三節  基本統計量分析……………………………	36
第四節  各變數單根檢定……………………………	38
第五節  門檻共整合及門檻效果檢定………………	39
第六節  門檻誤差修正模型領先關係檢定…………	44
第五章  研究結論與建議……………………………	58
第一節  研究結論……………………………………	58
第二節  後續研究建議………………………………	60
參考文獻 ………………………………………………	61
                   圖    目    錄
圖1.1.1  EUR/USD即期匯率與隱含波動率歷史走勢……………	2
圖1.1.2  EUR/USD歷史波動率與隱含波動率歷史走勢…………	2
圖1.3.1  研究流程………………………………………………	4
圖2.2.1  EUR/USD 1個月期Volatility Smile變化……………	10
圖2.2.2  EUR/USD Volatility Cone……………………………	10
圖2.2.3  EUR/USD Volatility Surface………………………	11
圖2.3.1  Straddle pay-off隨spot之變化（到期日）………	15
圖2.3.2  Straddle delta隨spot之變化（交易日）…………	16
圖2.3.3  Straddle gamma隨spot之變化（交易日）…………	16
圖2.3.4  RR pay-off隨spot之變化（到期日）………………	18
圖2.3.5  RR delta隨spot之變化（交易日）…………………	18
圖2.3.6  RR gamma隨spot之變化（交易日）…………………	19
圖2.3.7  BF pay-off（到期日）………………………………	20
圖2.3.8  ATM，RR and BF in Volatility Smile……………	21
圖2.3.9  Straddle vega隨spot之變化…………………………	24
圖2.3.10  Straddle vomma隨spot之變化………………………	24
圖2.3.11  Straddle vanna隨spot之變化………………………	25
圖2.3.12  Straddle delta隨spot與時間之變化………………	25
圖2.3.13  Straddle gamma隨spot與時間之變化………………	26
圖4.1.1   SPOT、RR、BF、ATM、HMA 及 HGA走勢圖……………34
圖4.5.1  S & ATM之MTAR門檻值τ=-0.011………………………42
圖4.5.2  S & R之MTAR門檻值τ=-0.003…………………………	43
圖4.5.3  S & B之TAR門檻值τ=0.079……………………………	43
圖4.5.4  ATM & HGA 之MTAR門檻值τ=-0.054……………………43
圖4.5.5  ATM & HMA 之MTAR門檻值τ=-0.390……………………43
                        表    目    錄
表2.3.1  匯率選擇權波動率市場報價…………………………	14
表4.2.1  GARCH（1，1）模型係數估計…………………………	35
表4.3.1  各變數敘述性統計資料………………………………	37
表4.4.1  KSS單根檢定結果………………………………………	38
表4.4.2  KPSS單根檢定結果……………………………………	38
表4.5.1  門檻自我迴歸模型選擇、門檻共整合與門檻效果檢定41
表4.6.1  誤差修正模型估計（即期匯率與ATM隱含波動率）…	46
表4.6.2  誤差修正模型估計（即期匯率與25D Risk Reversal）48
表4.6.3  誤差修正模型估計（即期匯率與25D Butterfly）…	50
表4.6.4  誤差修正模型估計（ATM隱含波動率與GARCH歷史波動率）52
表4.6.5  誤差修正模型估計（ATM隱含波動率與簡單移動平均歷史波動率）    ………………………………………………………	55

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