個股選擇權隱含波動率之研究

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姓名

廖子翔(Tzu-Hsiang Liao) 查詢紙本館藏

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財務金融學系

論文名稱

個股選擇權隱含波動率之研究
(Essays on Implied Volatility of Individual Stock Options)

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摘要(中)

本研究是由二篇有關於個股選擇權隱含波動率之文章所構成。
第一篇文章所研究的是關於套利風險對於個股選擇權之隱含波動率曲線斜率的影響。如果套利風險會影響隱含波動率曲線的斜率，則個股選擇權與套利風險之間是有關連的。實證結果顯示套利風險的確會影響到個股選擇權的隱含波動率曲線。當套利風險愈大時，隱含波動微笑的情形會愈明顯。藉由分開探討價外的賣權及買權，發現有些套利風險的影響是非對稱的。此外，投資人所抱持的信念差異也與套利風險有關。
第二篇文章的研究重點在於選擇權隱含波動率曲線不同模型之間的比較。在過去一、二十年間，有許多關於選擇權市場中隱含波動率模型估計的爭論。然而，在文獻上卻很少發現隱含波動率模型的比較，原因就在於缺乏一個理論基論。在此文章中，採用了組合虛無假設檢定的方法來比較不同的隱含波動模型。據目前所知，這是首次利用組合檢定的方法來探討此爭論的研究。實證結果顯示線性分段模型是最適合隱含波動微笑的模型。

摘要(英)

This study contains two essays in implied volatility of individual stock options. The first essay examines the effect of arbitrage risk on the slope of implied volatility curve for individual stock options. If arbitrage risk affects the slope of implied volatility curve, then there is a connection between stock options and arbitrage risk. The empirical results reveal that arbitrage risk does affect the slope of the implied volatility curve for stock options. The implied volatility smile is more pronounced for stocks with higher arbitrage risk. In addition, the longer the maturity of the option, the smaller the effect. By investigating the slopes for OTM puts and OTM calls, some effects of the arbitrage risk on the implied volatility curve are asymmetric.
The second essay focuses on the comparison among models of implied volatility curve of the stock options. Over the past few decades, there are many issues associated with the implied volatility smile in the options market. However, no much works have been found in the literature regarding the comparison of implied volatility models because lacking a theoretical foundation on which the comparative investigation could be conducted. In this essay, the methods for combining hypothesis tests are used to compare different implied volatility models. The empirical result shows that the linear piecewise model is the most appropriate model for implied volatility curves.

關鍵字(中)

★ 組合檢定
★ 隱含波動微笑
★ 非涵蓋模型
★ 套利風險
★ 反常態法
★ 反卡方法

關鍵字(英)

★ inverse normal method
★ arbitrage risk
★ implied volatility smile
★ combination test
★ non-nested model
★ inverse chi-square method

論文目次

Contents.................................................................................................................... i
List of Tables............................................................................................................ iii
List of Figures.......................................................................................................... v
Essay 1: Arbitrage Risk and Volatility Smile in Individual Stock Options....... 1
1 Introduction........................................................................................................... 2
2 Arbitrage Risk Proxies.................................................................................................... 4
2.1 Fundamental Risk.................................................................................................. 4
2.2 Noise Trader Risk.................................................................................................. 5
2.3 Implementation Risk.............................................................................................. 5
2.4 Firm-Specific Variables......................................................................................... 6
3 Data and Methodology.................................................................................................... 7
4 Empirical Results............................................................................................................ 10
5 Robustness Check........................................................................................................... 18
6 Conclusion...................................................................................................................... 28
References............................................................................................................................. 28
Essay 2: Fitting and Testing for Implied Volatility Curve with
Parametric Models.......................................................................... 32
1 Introduction........................................................................................................... 33
2 Implied Volatility Models and Non-nested Hypotheses................................................. 36
2.1 Implied Volatility Models...................................................................................... 36
2.2 Non-nested Hypotheses.......................................................................................... 38
2.3 Non-nested Testing Procedure............................................................................... 39
3 Combination Test............................................................................................................ 42
3.1 Inverse Chi-square Method.................................................................................... 42
3.2 Inverse Normal Method......................................................................................... 45
4 Data................................................................................................................................. 46
5 Empirical Results............................................................................................................ 47
5.1 Preliminary Results................................................................................................ 48
5.2 Combination Tests................................................................................................. 50
5.3 Robustness Checks................................................................................................ 57
6 Conclusion...................................................................................................................... 61
References............................................................................................................................. 64

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指導教授

周賓凰、張傳章
(Pin-Huang Chou、Chuang-Chang Chang)

審核日期

2008-6-26

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