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研究生： 郭美美
Mei-Mei Kuo
論文名稱： 選擇權價格隱含之風險與利率期限結構之預測
Impoied Risk in Option Prices and Forecating Term Structure of Swap Rates
指導教授： 林丙輝
Bing-Huei Lin
林孟彥
Tom M.Y. Lin
口試委員: 劉代洋
Day-Yang Liu
洪茂蔚
Mao-Wei Hung
張傳章
Chuang-Chang Chang
葉仕國
Shih-Kuo Yeh
王之彥
Jr-Yan Wang
莊文議
Wen-I Chuang
學位類別： 博士
Doctor
系所名稱： 管理學院 - 企業管理系
Department of Business Administration
論文出版年： 2012
畢業學年度： 100
語文別： 英文
論文頁數： 75
中文關鍵詞： 選擇權 、系統風險 、奇異風險 、資本資產訂價模式 、風險中立評價模式 、期限結構 、主成分分析法 、交換利率
外文關鍵詞： System risk, Option price, Idiosyncratic risk, Risk-neutral valuation relationship, term structure, swap rate
相關次數： 點閱：330  下載：1 
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    • 本論文主要是由兩篇論文所組成，分別為Chapter 1的 Implied systematic and idiosyncratic risk in option prices 與 Chapter 2的 Forecasting term structure of HIBOR swap rates，茲分別摘要如下:
    本論文之Chapter 1 主要是從Siegel (1995) 和 Husmann 與 Stephen (2007) 得到啟發，提出一個可以從選擇權價格資訊裡面，估計出系統風險 (system risk) (亦即β)與奇異風險 (idiosyncratic risk) 的嶄新方法。藉由 Stapleton 與 Subrahmanyam (1984) 和 Camara (2003)的市場模式 (market model) 與多變數風險中立評價關係 (multivariate risk-neutral valuation relationship)，本研究推導出了一個全新的隱含個股系統風險與奇異風險的個股選擇權評價模式。根據這個個股選擇權評價模式，我們是可以直接從市場指數選擇權與個股選擇權的市價中估計出隱含的β，而不是像傳統估計β的方法，是從歷史股價估計而來的。
    本研究所導出的選擇權定價模型可以解釋隱含波動率的微笑 ( volatility smile) 曲線與期限結構 (term structure)，而從美國 Dow Jones 30 index 成分股的實證上亦顯示此模型不僅可以提供一個β合理的估計值，且其估計的效率亦較傳統的β估計方法還來得優異。另外，實證結果也指出本論文所估計出的隱含β與傳統估計法的歷史β (historical beta) ，隱含β(implied β) 的資訊內涵是不同於歷史β (historical β)。
    本論文之Chapter 2 主要是針對香港交換利率 (HIBOR swap rates) 提出一個最適的交換利率期限結構 (term structure of interest rates) 的預測模型。我們藉由11種動態(dynamic) 模型，來預測香港交換利率期限結構，並從中以實證方法得到最適的預測模型，而這11種模型則包括了著名的Nelson-Siegel factors model、主成分分析法 (principal components analysis)等等。此外，我們也更進一步用實證方式評估各種模型對HIBOR swap yield curve 的level, slope, and curvature factors 的預測能力。實證結果顯示，Nelson-Siegel model 結合 autoregressive process on factor changes 的模型是預測 HIBOR swap yields與其level, slope, and curvature factors最有效率的模型。

    In Chapter 1, inspired from Siegel (1995) and Husmann and Stephen (2007), this study proposes a novel method to estimate β. Through combining the market model and the multivariate risk-neutral valuation relationship (RNVR) in Stapleton and Subrahmanyam (1984) and Camara (2003), we develop a pricing model for individual stock options involving the volatility of the market index level and the levels of the β and the idiosyncratic risk of the underlying stock asset. Based on this option pricing model, it is possible to estimate values of β implicitly based on the current prices of index options and individual stock options rather than based on the historical stock prices in the traditional method. The proposed option pricing model can explain the phenomena of volatility smiles and term structures, and the empirical studies in this study show that this novel method to estimate β can provide not only reasonable estimates of β but also perform better than the traditional method to predict the realized value of β in future periods of time.
    In Chapter 2, to investigate yield curve dynamics, researchers have employed a wide variety of models, including the famous Nelson-Siegel level, slope, and curvature factors, and principal components analysis, among others. In this study, we decompose the term structure of HIBOR (Hong Kong Interbank Offered Rate) swap rates by means of the Nelson-Siegel factors and principal components analysis, and employ autoregressive and vector autoregressive for ex ante forecasting the yield curve by predicting the dynamic factors and components. We compare the results of a broadly empirical prediction with benchmark models such as random walk and yield levels. Further, we survey the predictability in the shape of the swap yield curve for these models. Our results appear to show that the Nelson-Siegel model with autoregressive process on factor changes is the most efficient model for forecasting HIBOR swap yields.

    目 錄 中文摘要 --- Ⅰ 英文摘要 III 誌　　謝 V List of Figures IX List of Tables ---------------------------------------------------------------X Chapter 1 Implied Systematic and Idiosyncratic Risk in Option Prices 1.1 Introduction -----------------------------------------------------------1 1.1.1 Motives and Purposes---------------------------------------------1 1.1.2 Outline of the Study-----------------------------------------------6 1.2 Literature Review-----------------------------------------------------7 1.3 The Option Pricing Model Involving β--------------------------- 11 1.3.1 Distributions of Underlying Variables and the Aggregate Wealth--------------------------------------------------------------11 1.3.2 The Risk Neutral Valuation Relationship --------------------13 1.3.3 Deriving the Pricing Formula for European Calls ---------- 15 1.4 Explaining Black-Scholes Implied Volatility Patterns Using Our Option Pricing Model ---------------------------------------------- 18 1.5 Empirical Studies----------------------------------------------------25 1.5.1 Data Description------------------------------------------------- 25 1.5.2 Calibration Procedures ------------------------------------------29 1.5.2.1 Calibration of Implied σm---------------------------------29 1.5.2.2 Calibration of Implied β and Implied σe----------------30 1.5.3 Empirical Results-------------------------------------------------32 1.5.3.1 Forecasting Performance of the Implied β------------ 34 1.5.3.2 Competitive Regression between the Implied and Historical β---------------------------------------------- 37 1.5.3.3 Forecasting Performance of the Implied σe----------- 39 1.6 Conclusions------------------------------------------------------------ 43 Chapter 2 Forecasting Term Structure of HIBOR Swap Rates 2.1 Introduction-------------------------------------------------------------45 2.1.1 Motives and Purposes--------------------------------------------45 2.1.2 Outline of the Study----------------------------------------------46 2.2 Literature Review------------------------------------------------------47 2.3 Methodology -----------------------------------------------------------50 2.3.1 Data Description--------------------------------------------------50 2.3.2 Models -------------------------------------------------------------50 2.4 Empirical Results and Discussion -----------------------------------56 2.4.1 Forecasting Results-----------------------------------------------57 2.4.2 Comparison of Forecasting Performance of the Shapes of the Swap Yield Curves---------------------------------------------- 61 2.5 Conclusion --------------------------------------------------------------64 Reference ----------------------------------------------------------------------66 Appendix I --------------------------------------------------------------------71 Appendix II -------------------------------------------------------------------74 作者簡 介-----------------------------------------------------------------------75 授 權 書-------------------------------------------------------------------------76

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