在 Black-Sholes 模型下運用選擇權資料進行動態避險之比較

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沈睿謙(Rui-Qian Shen) 查詢紙本館藏

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統計研究所

論文名稱

在 Black-Sholes 模型下運用選擇權資料進行動態避險之比較
(Comparisons of dynamic hedging of financial options using different volatility estimators under the Black-Scholes model)

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摘要(中)

投資人對於未來有很多觀點，所以許多學者在Black-Scholes 模型下利用選擇權資料去估計波動度。本文提供了一個在Black-Scholes 模型下估計波動度的方法。在我們的方法中，我們考慮了一個在Black-Scholes 模型下利用所有選擇權資料以及廣義線性回歸去估計波動度。之後，用估計出來的波動度去計算Greeks 並且對不同履約價的TAIEX 選擇權做動態避險。實證分析的結果顯示，我們所使用的避險方法優於其他的指標，也就是說，利用隱含波動或是歷史log return 的標準差。

摘要(英)

Options contain many investor’s future views toward future, thus many scholars estimate the volatility in Black-Scholes model by using option data. In this thesis, we provide a method to estimate volatility under Black-Scholes model. In our method, we consider a generalized linear regression to estimate the volatility under the Black-Scholes model by using all options. Afterwards, we use the estimated volatility to calculate Greeks and do dynamic hedging for TAIEX options at different strike price. The empirical results show that hedging using this method outperforms other benchmark methods, i.e., using
implied volatilities or using standard deviations of historical log returns.

關鍵字(中)

★ Greeks
★ 動態避險
★ Delta vega 避險
★ Delta 避險
★ 牛頓法

關鍵字(英)

★ Greeks
★ Dynamic hedge
★ Delta vega hedge
★ Delta hedge
★ Newton method

論文目次

摘要i
Abstract ii
誌謝iii
List of Figures vi
List of Tables vii
1 Introduction 1
2 Methodology 4
3 Simulation studies 7
4 Empirical Analysis 9
4.1 Exploratory data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4.2 Dynamic hedging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
5 Dynamic Hedging Result 18
5.1 Delta Hedge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.2 Delta Vega Hedge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
6 Conclusion 32
References 33

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指導教授

鄧惠文(Huei-Wen Teng)

審核日期

2015-8-12

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