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研究生:陳明憲
研究生(外文):Ming-Hsien Chen
論文名稱:費城交易所外匯選擇權隱含波動資訊效果與預測能力之研究
論文名稱(外文):The Predictive Power of Implied Stochastic Volatility in PHLX Currency Options Market
指導教授:楊聲勇楊聲勇引用關係高櫻芬高櫻芬引用關係
指導教授(外文):Sheng-Yung YangYin-Feng Gau
學位類別:碩士
校院名稱:國立暨南國際大學
系所名稱:國際企業學系
學門:商業及管理學門
學類:企業管理學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:88
中文關鍵詞:外匯選擇權隱含波動隱含隨機波動預測資訊內容
外文關鍵詞:volatilityimplied volatilityimplied stochastic volatilityinformation contentforecastingcurrency option
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從選擇權定價理論分析,選擇權的交易即是對資產價格波動的交易。
若選擇權市場是具效率性的,則未來現貨價格波動的預期皆已反映在選擇權的交易資訊中。然而,如何精確地估計金融資產價格的波動,是相當困難的,因而過去有許多學者致力於波動的衡量 (specification) 與預測的實證研究。此乃源自金融資產價格的波動,無論在選擇權定價領域抑或風險管理的相關課題,皆扮演相當關鍵的角色。直此,本論文之主要目的在:第一,研究選擇權市場的資訊內容 (information content),即交易價格是否充分反應對未來金融資產價格波動的預期;第二,比較時間數列模型與選擇權定價模型中的隱含波動 (implied volatility) 二者之間,對於資產價格實際波動 (realized volatility) 的預測能力。時間數列模型包含指數平滑法 (exponential smoothing method) 與 GARCH 模型;而隱含波動則從Black and Scholes type 並適用於外匯選擇權的Garman and Kohlhagen (1983) 定價模型,與Hull and White (1987) 的隨機選擇權定價模型中反導而得。
本文實證對象為費城交易所美式外匯選擇權,包括英鎊、德國馬克、日圓與瑞士法郎等四種外匯,研究期間則自1994年至2001年共計約19萬筆交易資料。實證結果顯示,四種外匯選擇權的隱含波動皆具有資訊效果,此實證結果顯示,費城交易所市場參與者能充分反應出,對未來匯率波動的預期並將之運用到選擇權的交易上。而對實際波動的預測能力,經由實證結果發現,隱含波動對實際波動的預測較指數平滑法與GARCH等時間數列模型為佳,其中由Garman and Kohlhagen (1983) 定價模型所推導的隱含波動在德國馬克與日圓的預測的精確性優於Hull and White (1987) 的隱含隨機波動;而在英鎊與瑞士法郎則呈現相反的結果。本文的貢獻,除了延續 Jorion (1995) Xu and Taylor (1995) 與 Guo (1996) 針對外匯選擇權的資訊效果與預測能力的研究,並同時比較 Black and Scholes 假定資產價格的波動為常數下所反導之隱含波動,與波動模式服從隨機過程下的隱含隨機波動 (implied stochastic volatility)。而在實務應用上,可以此實證結果,進行外匯選擇權的評價並形成較佳的避險策略,以為實務界參考。
If the expectation formation in options markets reflects all the currently available information on the future price movements, option prices will be useful in forecasting the price fluctuation of underlying assets. Numerous research has been devoted to the specification of volatility and its measurement, though modeling the volatility is a difficult task. Because of the central role that volatility plays in derivation valuation and risk management, the thesis investigates various volatility measures, including exponential smoothing model, GARCH process, Garman and Kohlhagen (1983) implied volatility and Hull and White implied stochastic volatility, and their predictive power in currency market.
We investigates the information content and the predictive power of implied stochastic volatility in four PHLX currency options, including British pound, Deutsche mark, Japanese yen and Swiss franc, over the period from January 1994 to December 2001 by using a various volatility estimation procedures. In contrast of prior research, we extend the method of Jorion (1995) who just uses the Black and Scholes type and European-style option and extend the studying period of Guo (1996) to the period from 1994 to 2001.
Empirical results show that traders in Philadelphia currency options market uses the information effectively and reflect these volatility expectation to trade options by option pricing models. The Philadelphia currency options market is informationally efficient in setting prices and the volatility implicit in option prices provide superior predictors of future volatility than time series models. Furthermore, we can take the implied volatility measures to form the better hedging strategy for financial institutions, multinational corporations and individuals in practice.
Contents
Contents Ⅰ
Table Index Ⅲ
Figure Index Ⅳ
Chapter 1. Introduction 1
1.1 Research Motivation 1
1.2 Research Objectives 4
Chapter 2. Literature Review 9
2.1 Historical Volatility Estimation 11
2.1.1 Unconditional Volatility Measures 11
2.1.2 Conditional Volatility Models 14
2.2 Options Pricing Models 18
2.2.1 Black and Scholes Type Constant Volatility Models 18
2.2.2 Stochastic Volatility Option Pricing Model 21
2.3 Review on Related Empirical Studies 25
Chapter 3. Research Methodology 29
3.1 Data Description 29
3.2 The Estimation of Volatility 35
3.2.1 Daily Realized Volatility 35
3.2.2 The Exponential Smoothing and GARCH Conditional Volatility 36
3.2.3 The Estimation Procedure of Implied Volatility 37
3.2.4 An Approximation Method of American Style Option 41
3.3 Tests of Information Content 45
3.4 The Evaluation of Predictive Power of Volatility 47
Chapter 4. Empirical 54
4.1 The Descriptive Statistics of Various Volatility Measures 54
4.2 The Information Content of Implied Volatility and In-Sample Testing 64
4.3 The Predictive Power of Implied Volatility 69
Chapter 5. Conclusion 76
Appendix 79
A1. Algorithm for Barone-Adesi and Whaley (1987) American Option Pricing Model (for MATLAB software) 79
A2. Algorithm for Approximation model of Hull and White (1987) European Stochastic Volatility Option Pricing Model (for MATLAB software) 81
A3. Algorithm for calculating Whaley (1982) equally-weighted nonlinear squares method to derive the implied volatility (for MATLAB software) 83
References 84
Table Index
Table 3-1 Samples of Currency Options 32
Table 3-2 Descriptive Statistics of Foreign Exchange Spot Rates 32
Table 4-1.1 Summary Statistics for Volatility Measure (British pound) 58
Table 4-1.2 Summary Statistics for Volatility Measure (Deutsche mark) 59
Table 4-1.3 Summary Statistics for Volatility Measure (Japanese yen) 60
Table 4-1.4 Summary Statistics for Volatility Measure (Swiss franc) 61
Table 4-2.1 Testing the Information Content of Implied Volatility (BP) 67
Table 4-2.2 Testing the Information Content of Implied Volatility (DM) 67
Table 4-2.3 Testing the Information Content of Implied Volatility (JY) 68
Table 4-2.4 Testing the Information Content of Implied Volatility (SF) 68
Table 4-3 Predictive Power of Volatility: Regression Analysis 73
Table 4-4 Predictive Power of Volatility: Out-of-Sample Forecasting Errors 74
Table 4-5 The Forecast-Accuracy Comparison of Predicted Volatilities 75
Figure Index
Figure 1 The Patterns of Spot Rate and the Daily Returns of Four Currencies 34
Figure 2 Realized Volatility, Exponential Smoothing Volatility, GARCH Volatility, and Implied Volatility 62
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