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研究生:陳菁華
研究生(外文):Ching-Hua Chen
論文名稱:利用快速傅立葉轉換於跳躍-發散與隨機波動模型之選擇權最適避險策略
論文名稱(外文):Optimal Option Hedging Strategy with Fast Fourier Transform in Jump Diffusion and Stochastic Volatility Models
指導教授:涂登才涂登才引用關係陳琪龍陳琪龍引用關係
指導教授(外文):Teng-Tsai TuMax Chen
學位類別:碩士
校院名稱:銘傳大學
系所名稱:財務金融學系碩士班
學門:商業及管理學門
學類:財務金融學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:中文
論文頁數:140
中文關鍵詞:快速傅立葉轉換跳躍-發散隨機波動條件風險值避險Delta-Gamma中立避險
外文關鍵詞:Jump-DiffusionStochastic VolatilityFast Fourier TransformDelta-Gamma NeutralConditional VaR Hedge
相關次數:
  • 被引用被引用:7
  • 點閱點閱:564
  • 評分評分:
  • 下載下載:120
  • 收藏至我的研究室書目清單書目收藏:0
Black-Scholes模型存在假設選擇權之標的資產為對數常態分配及假設波動率隨時間經過並不會改變之兩個主要缺陷。因此,為改良Black-Scholes模型之缺陷、加快選擇權評價速度以及使買權價格函數為一平方可積函數等目的,本研究嘗試利用快速傅立葉轉換為媒介於Merton (1976)跳躍-發散模型、Heston (1993)隨機波動模型及Bates (1996)跳躍-發散與隨機波動之混合模型等三種修正模型,以進行臺指選擇權評價,並建構運用於不同商品下之選擇權避險策略。本研究於現貨商品避險方面採用傳統Delta中立避險與Delta-Gamma中立避險,至於衍生性商品避險方面則採用最小避險風險法及最適CVaR避險策略。最後,更進一步與對照組Black- Scholes模型比較分析不同選擇權評價模型及不同避險策略於五日、十日及二十日避險區間之績效表現,並決定何種避險模型及避險策略可得最佳之避險效果。
根據選擇權避險之實證結果顯示,關於現貨商品避險方面,臺指價內買權或賣權避險策略運用以Delta中立避險效果較佳;股價波動幅度較大之價平及價外選擇權則以採用Delta-Gamma中立避險策略較為合適。其次,隨著避險區間之增長,各模型與策略之避險績效愈佳。至於衍生性商品避險方面,最小避險風險法大抵而言顯著相對優於最適CVaR避險策略,且整體而言信賴水準愈高的最適CVaR避險策略其避險績效愈佳。
Two major disadvantages in the conventional Black-Scholes model include that the underlying asset follows the log normal distribution and that volatility of underlying asset does not vary over time. To overcome these disadvantages, speed up option valuation and obtain call pricing function be a square-integrable function, this study employs fast Fourier transform in three modified call option valuation models, i.e., the jump-diffusion (Merton) model, stochastic volatility (Heston) model, and stochastic volatility with jump (SVJ, Bates) model. These models are utilized to assess TAIEX options and to formulate option hedging strategy. The traditional Delta neutral and Delta-Gamma neutral option hedging strategies are used to hedge the underlying assets. Furthermore, the minimizing hedge risk and optimal Conditional VaR methods are used to hedge the portfolio of derivative assets.
The empirical results of option hedging on spot market indicate that the Delta Neutral strategy of hedging in-the-money TAIEX options obtains better hedging effectiveness. When at-the-money and out-of-the-money TAIEX options with large volatility are used as hedging instruments, Delta-Gamma Neutral strategy obtains better hedging effectiveness. Moreover, the hedging effectiveness of various models and strategies increases as hedging horizon increases. As to options hedging on derivative assets, the hedging effectiveness of minimizing hedge risk outperformed that of optimal Conditional VaR hedge. The higher the confident level, the higher the hedging effectiveness of optimal Conditional VaR Hedge.
第壹章 緒論 1
第一節 研究背景與動機 1
第二節 研究目的 7
第三節 研究架構 8
第貳章 文獻回顧 10
第一節 選擇權評價之相關文獻 10
第二節 選擇權避險之相關文獻 20
第參章 研究設計與方法 26
第一節 股價隨機過程 26
第二節 選擇權之評價 34
第三節 選擇權之風險係數(Greeks) 47
第四節 選擇權避險策略 52
第肆章 實證分析 63
第一節 資料來源與臺指選擇權之敘述統計分析 63
第二節 選擇權評價與分析 70
第三節 現貨商品之選擇權避險策略運用 80
第四節 衍生性商品之選擇權避險策略運用 106
第伍章 結論與建議 118
第一節 結論 118
第二節 後續研究之建議 124
參考文獻 125


圖目錄
圖1-1 1 研究架構流程圖 9
圖4-1 1 2007年9月3日至2008年2月29日之近月臺指買權結算價走勢 66
圖4-1 2 2007年9月3日至2008年2月29日之近月臺指賣權結算價走勢 66
圖4 1 3 2007年9月3日至2008年2月29日之次近月臺指買權結算價走勢 67
圖4-1 4 2007年9月3日至2008年2月29日之次近月臺指賣權結算價走勢 67
圖4 1 5 2007年9月3日至2008年2月29日之遠月臺指買權結算價走勢 68
圖4-1 6 2007年9月3日至2008年2月29日之遠月臺指賣權結算價走勢 68



























表目錄
表 1-1 1 近年國內期貨與選擇權成交量統計表 單位:口 2
表 3-3 1 訂價決定因子與買賣權之關係 47
表 4-1 1 2007年9月3日至2008年2月29日內不同到期日及價性下臺指選擇權結算價之敘述統計量 69
表 4-2-1 跳躍-發散、隨機波動及混合模型於研究期間內買權最適參數估計之均值 72
表 4-2 2 跳躍-發散、隨機波動及混合模型於研究期間內賣權最適參數估計之均值 72
表 4-2 3 四種模型於樣本外整體買權評價誤差之Wilcoxon符號等級檢定值 75
表 4-2 4 四種模型於樣本外整體賣權評價誤差之Wilcoxon符號等級檢定值 76
表 4-2 5 不同誤差績效分析下樣本外整體選擇權評價之最佳模型彙總 77
表 4-2 6 樣本外整體買權及賣權評價誤差之Wilcoxon符號等級檢定值 79
表 4-3 1 Delta中立避險運用於四種模型之臺指近月選擇權平均避險績效 82
表 4 3 2 Delta中立避險下四種模型於臺指近月選擇權避險績效之Wilcoxon符號等級檢定值 83
表 4 3 3 Delta中立避險運用於四種模型之臺指次近月選擇權平均避險績效 85
表 4 3 4 Delta中立避險下四種模型於臺指次近月選擇權避險績效之Wilcoxon符號等級檢定值 86
表 4 3 5 Delta中立避險運用於四種模型之臺指遠月選擇權平均避險績效 88
表 4 3 6 Delta中立避險下四種模型於臺指遠月選擇權避險績效之Wilcoxon符號等級檢定值 90
表 4 3 7 Delta中立避險運用於四種模型之臺指整體選擇權平均避險績效 91
表 4 3 8 Delta中立避險下四種模型於臺指整體選擇權避險績效之Wilcoxon符號等級檢定值 93
表 4 3 9 Delta-Gamma中立避險運用於四種模型之臺指選擇權平均避險績效 95
表 4 3 10 Delta-Gamma中立避險下四種模型於臺指選擇權的避險績效之Wilcoxon符號等級檢定值 96
表 4 3 11 個別模型於不同到期日Delta中立避險策略之價內選擇權避險績效之Wilcoxon符號等級檢定值 98
表 4 3 12 個別模型於不同到期日Delta中立避險策略之價平選擇權避險績效Wilcoxon符號等級檢定值 99
表 4 3 13 個別模型於不同到期日Delta中立避險策略之價外選擇權避險績效之Wilcoxon符號等級檢定值 100
表 4 3 14 個別模型於現貨商品避險策略下臺指買權與臺指賣權避險績效之Wilcoxon符號等級檢定值 101
表 4 3 15 個別模型於現貨商品避險策略下臺指選擇權的避險績效之Wilcoxon符號等級檢定值 103
表 4 4 1 最小避險風險法運用於四種模型之臺指選擇權平均避險績效 108
表 4 4 2 最小避險風險法下四種模型於臺指選擇權的避險績效之Wilcoxon符號等級檢定值 109
表 4 4 3 最適CVaR避險運用於四種模型之臺指選擇權平均避險績效 111
表 4 4 4 最適CVaR避險下四種模型於臺指選擇權的避險績效之Wilcoxon符號等級檢定值 112
表 4 4 5 個別模型於衍生性商品避險策略下臺指買權與臺指賣權避險績效之Wilcoxon符號等級檢定值 114
表 4 4 6 個別模型於衍生性商品避險策略下臺指選擇權的避險績效之Wilcoxon符號等級檢定值 115
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