臺灣博碩士論文加值系統

Fleming(1998a)使用S&P 100 指數選擇權去探討隱含波動是否為股票市場波動的一個不偏預測及隱含波動的預測誤差是否和市場上資訊集成正交關係。其實証結果顯示，隱含波動是一個有偏誤的估計式，而且總是有高估的現象。在不考慮隱含波動是一偏誤的估計式下，使用隱含波動的線性模型來預測市場波動具有不錯的結果。隱含波動的預測誤差和條件波動模型（包括歷史波動模型及GARCH(1,1)模型）具有正交的關係，也就是說隱含波動不能去解釋波動預測誤差的部份，歷史波動模型和GARCH(1,1)模型也不能去解釋。
本文試著去解釋造成隱含波動會是一偏誤估計式的原因。這可能是因為在選擇權評價模式中對波動過程假設有偏誤及一些衡量誤差，也可能是因為選擇權市場沒效率使然。然而即使選擇權市場是有效率的，但選擇權的價格也可能會因為交易成本及一些市場不完全因素而偏離其理論價格。本文認為台灣認購權証市場中隱含波動會是一偏誤估計式的是由於券商的發行成本及選擇權市場沒效率所造成的。
由於利用Black-Scholes模型所反推之隱含波動有衡量誤差之問題，本文利用二階段最小平方法來做波動預測能力之檢驗，並試著去找出真實隱含波動的最佳估計式。此外，本文對S＆P100股價指數選擇權進行週資料和月資料的分析以瞭解美國選擇權市場各波動模型的比較結果。
在台灣認購權証市場中，由週資料實証結果顯示隱含波動不具預測波動之資訊內涵。相較於台灣市場，S&P100指數選擇權，其隱含波動較具資訊內涵。即使是使用二階段最小平方法修正後，台灣及美國市場的隱含波動仍是偏誤的估計式。雖然所有波動模型在兩國市場中都是偏誤的估計式，但在台灣認購權証市場中，不管是使用歷史波動模型或ARCH(5)波動模型或GARCH(1,1)波動模型去預測未來的波動都會比隱含波動來的佳。若用日波動資料來建構真實波動，則在大部份台灣認購權証市場的樣本資料中，ARCH(5)會是一個較好的波動預測模型。

Fleming(1998a) uses S&P100 index option to discuss whether implied volatility is an unbiased estimator of stock market volatility and whether the forecasting error of implied volatility and the market information set have orthogonal relationship. The empirical result indicates that implied volatility is a biased estimator , and it always produces higher estimation. Without the consideration that implied volatility is a biased estimator, using the linear model of implied volatility achieves a good result. The forecasting error of implied volatility and conditional volatility, including historical volatility model and GARCH(1,1) model, have orthogonal relationship. In other words, implied volatility model can''t explain the forecasting error of volatility, neither can historical model and GARCH(1,1) model.
The purpose of this thesis is to explain why implied volatility is a biased estimator. A possible reason is that there is a bias and measuring error in option pricing model. Another possible reason is that option market is inefficient. Even if option market is efficient, the price of option may deviate from theoretical price because of the trading cost and incomplete factor from market. The issuing cost of securities and the inefficiency of option market might explain that the implied volatility in Taiwan warrant market is a biased estimator.
Due to the measuring error of implied volatility deduced from Black-Scholes model, I adopt two-stage-least-square method to compare the ability of volatility forecasting and try to find out what is the best estimator of realized implied volatility. Furthermore, I also analyze the weekly and monthly data of S&P100 index option in order to understand the comparison result of each volatility model of U.S. option market.
In Taiwan warrant market, the weekly empirical result indicates that implied volatility doesn''t have any information about volatility forecasting. The implied volatility of S&P100 index option performs better than that of covered warrant in Taiwan market. Although modified by two-stage-least-square method, the implied volatility in Taiwan and U.S. market is still a biased estimator. In Taiwan warrant market, however, using ARCH(5) or GARCH(1,1) volatility model can make a better prediction than using implied volatility model. When daily data is used to construct realized volatility, ARCH(5) will be a better volatility forecasting model for most of the sample data in Taiwan warrant market.

第一章緒論1
第一節研究背景與動機1
第二節研究問題4
第三節研究目的6
第四節研究限制7
第五節研究架構.8
第二章文獻回顧10
第一節Black-Scholes的隱含波動10
第二節隱含波動是否為一良好的波動預測指標17
第三節隱含波動的預測品質(forecast quality)21
第四節交易策略(trading strategies)25
第三章研究方法29
第一節波動的估計29
第二節波動預測之相關計量方法40
第三節單根檢定(unit root test)與共整合關係的檢定47
第四章實證分析52
第一節資料來源及處理52
第二節不偏檢定56
第三節效率檢定和白噪音檢定67
第四節考慮下週股價漲跌的隱含波動69
第五節考慮修正隱含波動衡量誤差下的隱含波動預測能力70
第六節PP檢定76
第七節認購權證理論價格與實際市場價格之誤差78
第八節S＆P100股價指數選擇權市場實證結果分析79
第五章結論與建議84
第一節結論84
第二節建議89
附錄91
參考文獻96

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