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研究生:陳佑庭
研究生(外文):Yu-ting Chen
論文名稱:The Valuation of Reset Options when Underlying Assets are Autocorrelated
論文名稱(外文):The Valuation of Reset Options when Underlying Assets are Autocorrelated
指導教授:劉裕宏劉裕宏引用關係
指導教授(外文):Yu-hong Liu
學位類別:碩士
校院名稱:國立成功大學
系所名稱:財務金融研究所
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:英文
論文頁數:88
中文關鍵詞:Gamma跳躍Delta跳躍自我相關重設選擇權MA(q) process
外文關鍵詞:MA(q) processAutocorrelationDelta JumpReset OptionGamma Jump
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這篇論文的主要目的,是將標的資產的報酬自我相關特性納入重設選擇權的評價模型中。為了探討這種自我相關特性的影響程度,我們利用MA(q) process來表示標的資產價格變動的過程,而這個MA(q) process也是我們針對學者Liao和Chen在2006年所提及的MA(1) process所做的延伸。在這樣的資產價格變動過程下,報酬自我相關的特性不但會影響標的資產報酬的波動度,更會因此影響重設機率與重設選擇權的價值。如果標的資產報酬是正的自我相關,則會使重設機率增加,並使重設選擇權的價值上升;相反地,如果是負的自我相關,則會使重設機率和重設選擇權的價值下降。除此之外,我們也發現自我相關的特性會影響重設選擇權買方的重設時間點,當資產報酬呈現正的自我相關時,因為重設選擇權的波動度變大,為了避免可能的損失,重設選擇權的買方會傾向提早執行重設。最後,我們也發現自我相關的特性對於重設選擇權的避險效果有顯著的影響,如果標的資產報酬是正的自我相關,則可以減輕所謂的Delta跳躍和Gamma跳躍等避險問題。
This thesis mainly introduces the autocorrelation effect of asset returns into the valuation model of reset options.
The MA(q) process, which is an extension of the MA(1) process mentioned by Liao and Chen (2006), is applied to the valuation of reset options in this thesis. Due to the impact of autocorrelation on the volatility of asset returns, the probability of reset and the value of the reset option are affected. The positive autocorrelation increases the value of the reset option by increasing the probability of reset. Conversely, the negative autocorrelation decreases the probability of reset and reset premium. Moreover, the reset timing is also affected by the autocorrelation characteristic. When there is a positive autocorrelation, investors tend to reset earlier to avoid the possible loss. The impact of autocorrelation is also significantly on the hedging of reset options. This thesis demonstrates that the positive autocorrelation characteristic actually lessens the delta jump and gamma jump problems.
Contents

Chapter 1 Introduction...................................1
1.1 The Research Background and Objectives...............1
1.2 Structure of This Thesis.............................5

Chapter 2 Literature Review..............................6
2.1 Autocorrelation in the Returns of Financial Assets...6
2.2 Valuation of Options when Underlying Assets are Predictable...............................................7
2.3 Reset Right Embedded................................10
2.3.1 Reset Options with Holder Discretionarily Chosen Reset Time...............................................11
2.3.2 Reset Options with Automatically Triggered Reset..12

Chapter 3 Valuation Model of MA(q)-type Reset Options...18
3.1 Dynamic Process of Autocorrelated Asset Return......18
3.2 The Valuation of Standard Reset Options with a Single Reset Right under the MA(q) Process......................21
3.3 The Valuation of Standard Reset Options with Multiple Reset Rights under the MA(q) Process.....................24
3.4 The Valuation of Reset Options with m Reset Levels and Continuous Time under the MA(q) Process...........28
3.5 The Valuation of Standard Reset Bond Options with Multiple Reset Rights under the MA(1) Process............31

Chapter 4 Numerical Analyses of MA(1)-type Reset Options..................................................35
4.1 Effects on the Value of Reset Options...............35
4.2 Effects on the Reset Timing of Reset Options........44
4.3 Effects on the Delta and Gamma Jumps of Reset Options..................................................46

Chapter 5 Conclusions and Further Researches............55
5.1 Conclusions.........................................55
5.2 Further Researches..................................56

References...............................................58

Appendix A...............................................63

Appendix B...............................................68

Appendix C...............................................75

Appendix D...............................................82


List of Tables

Table 4.1 Comparison between Non-autocorrelated and MA(1)-type Reset Calls, with Three Reset Levels and One Month Reset Period.............................................42

Table 4.2 Comparison between Non-autocorrelated and MA(1)-type Reset Calls, with Three Reset Levels and Three Months Reset Period.............................................43

Table 4.3 Delta Gap Comparison of Three Reset Calls with Different Degrees of Positive Autocorrelation under Volatility 30%...........................................48

Table 4.4 Delta Gap Comparison of Three Reset Calls with Different Degrees of Positive Autocorrelation under Volatility 50%...........................................49

Table 4.5 Delta Gap Comparison of Three Reset Calls with Different Degrees of Negative Autocorrelation under Volatility 30%...........................................51

Table 4.6 Delta Gap Comparison of Three Reset Calls with Different Degrees of Negative Autocorrelation under Volatility 50%...........................................52


List of Figures

Figure 4.1 Value Comparison between Non-autocorrelated Standard Reset Put and MA(1)-type Standard Reset Puts when Time to Maturity is One Year.............................38

Figure 4.2 Value Comparison between Non-autocorrelated Standard Reset Put and MA(1)-type Standard Reset Puts when Time to Maturity is Two Years............................39

Figure 4.3 Value Comparison among Non-autocorrelated Standard, MA(1)-type Standard, and MA(2)-type Standard Reset Puts when Time to Maturity is One Year.............40

Figure 4.4 Optimal Reset Timing Comparison between the Non-autocorrelated Standard and MA(1)-type Standard Reset Puts.....................................................45

Figure 4.5 Delta Jumps of Three Reset Calls with Different Degrees of Positive Autocorrelation under Volatility 30%...........................................48

Figure 4.6 Delta Jump of Three Reset Calls with Different Degrees of Positive Autocorrelation under Volatility 50%......................................................49

Figure 4.7 Delta Jumps of Three Reset Calls with Different Degrees of Negative Autocorrelation under Volatility 30%...........................................51

Figure 4.8 Delta Jumps of Three Reset Calls with Different Degrees of Negative Autocorrelation under Volatility 50%...........................................52

Figure 4.9 Gamma Jumps of Three Reset Calls with Different Degrees of Autocorrelation under Volatility 30%......................................................54
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