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研究生:郭宗榮
研究生(外文):Tsung-Jung Kuo
論文名稱:遠期生效亞式選擇權之分析解-考慮隨機波動效果
論文名稱(外文):Analytic Formulae for Stochastic Volatility Forward-starting Asian Options
指導教授:林忠機林忠機引用關係
指導教授(外文):Lin, Chung-Gee
學位類別:碩士
校院名稱:東吳大學
系所名稱:商用數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:英文
論文頁數:94
中文關鍵詞:解析解遠期生效亞式選擇權蒙地卡羅模擬法隨機波動
外文關鍵詞:analytic solutionforward-starting Asian optionMonte Carlo simulationstochastic volatility
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遠期生效亞式選擇權的評價是很複雜的由於對數常態隨機變數的算術平均不再是對數常態。此外此時內含隨機波動特色的金融資產被廣泛地見證,任憑那些選擇權在實務應用上很流行,不過一些學術研究仍致力於隨機波動遠期生效亞式選擇權的評價與避險。本文擴展 Hull and White (1987) 的研究並結合泰勒展開式推導出考慮隨機波動之遠期生效亞式選擇權的解析解。當使用大樣本的蒙地卡羅模擬法為基準時,數值實驗證明我們的解析解成果很好並且在計算上有效率。針對隨機波動遠期生效亞式選擇權的評價與避險,我們的解析解也可以視為很實用的工具因為它很容易實行而且當計算速度是重要的考量時它是令人非常滿意的。
The valuation of forward-starting Asian options is complicated due to the fact that the arithmetic average of lognormal random variables is no longer lognormal. Furthermore, as the stochastic volatility features inherent in the financial asset prices are extensively witnessed, however, few academic works pay attention to the pricing and hedging of stochastic volatility forward-starting Asian options, despite the popularity of these options in practical application. This paper extends the study of Hull and White (1987) and integrates the Taylor series expansion for deriving analytic solution of forward-starting Asian options with stochastic volatility. Numerical experiments show that our analytic solution performs very well and is computationally efficient as benchmarked with large sample Monte Carlo simulations. Our analytic solution can also be treated as a practical tool for pricing and hedging stochastic volatility forward-starting Asian options, since it is easy to implement and is more desirable as the computing speed is an important consideration.
Contents
1. Introduction………………………………………………………………………..1
2. Literature Review
2.1. Reviewing Tsao, Cha, and Lin’s Model……………………...………………8
2.2. Reviewing Stochastic Volatility Model……………………………………..13
3. Model Assumption
3.1. Pricing formula………………………………………………………………16
3.2. Hedging Parameters…………………………………………………………23
4. Numerical Analysis……………………………………………………………….28
5. Conclusions……………………………………………………………………….42
Appendix…………………………………………………………………………….45
References…………………………………………………………………………...58
Table Contents
Table 1. Comparisons of forward-starting Asian call option between stochastic and constant volatility…………………………………………………..61
Table 2. Comparisons of forward-starting Asian call option between analytical solution and Monte-Carlo method……………………………………..62
Table 3. Comparisons of forward-starting Asian call option between analytical solution and Monte-Carlo method……………………………………..63
Table 4. Comparisons of forward-starting Asian call option between analytical solution and Monte-Carlo method……………………………………..64
Table 5. Comparisons of forward-starting Asian call option between analytical solution and Monte-Carlo method……………………………………..65
Table 6. Comparisons of forward-starting Asian call option between analytical solution and Monte-Carlo method……………………………………..66
Table 7. Comparisons of analytic solution forward-starting Asian call option between constant and stochastic volatility…………………………….67
Table 8. Comparisons of analytic solution forward-starting Asian call option between constant and stochastic volatility…………………………….68
Table 9. Comparisons of analytic solution forward-starting Asian call option between constant and stochastic volatility…………………………….69
Table 10. Comparisons of analytic solution forward-starting Asian call option between constant and stochastic volatility…………………………….70
Table 11. Comparisons of analytic solution forward-starting Asian call option between constant and stochastic volatility…………………………….71
Table 12. Comparisons of analytic solution forward-starting Asian call option between constant and stochastic volatility…………………………….72
Table 13. Comparisons of analytic solution forward-starting Asian call option between constant and stochastic volatility…………………………….73
Table 14. Comparisons of analytic solution forward-starting Asian call option between constant and stochastic volatility…………………………….74
Table 15. Comparisons of the delta value of forward-starting Asian call option between constant and stochastic volatility…………………………….75
Table 16. Comparisons of the delta value of forward-starting Asian call option between constant and stochastic volatility…………………………….76
Table 17. Comparisons of the delta value of forward-starting Asian call option between constant and stochastic volatility…………………………….77
Table 18. Comparisons of the delta value of forward-starting Asian call option between constant and stochastic volatility…………………………….78
Table 19. Comparisons of the delta value of forward-starting Asian call option between constant and stochastic volatility…………………………….79
Table 20. Comparisons of the delta value of forward-starting Asian call option between constant and stochastic volatility…………………………….80
Table 21. Comparisons of the delta value of forward-starting Asian call option between constant and stochastic volatility…………………………….81
Table 22. Comparisons of the delta value of forward-starting Asian call option between constant and stochastic volatility…………………………….82
Table 23. Comparisons of the gamma value of forward-starting Asian call option between constant and stochastic volatility…………………………….83
Table 24. Comparisons of the gamma value of forward-starting Asian call option between constant and stochastic volatility…………………………….84
Table 25. Comparisons of the gamma value of forward-starting Asian call option between constant and stochastic volatility…………………………….85
Table 26. Comparisons of the gamma value of forward-starting Asian call option between constant and stochastic volatility…………………………….86
Table 27. Comparisons of the vega value of forward-starting Asian call option between constant and stochastic volatility…………………………….87
Table 28. Comparisons of the vega value of forward-starting Asian call option between constant and stochastic volatility…………………………….88
Table 29. Comparisons of the vega value of forward-starting Asian call option between constant and stochastic volatility…………………………….89
Table 30. Comparisons of the vega value of forward-starting Asian call option between constant and stochastic volatility…………………………….90
Table 31. Comparisons of the vega value of forward-starting Asian call option between constant and stochastic volatility…………………………….91
Table 32. Comparisons of the vega value of forward-starting Asian call option between constant and stochastic volatility…………………………….92
Table 33. Comparisons of the vega value of forward-starting Asian call option between constant and stochastic volatility…………………………….93
Table 34. Comparisons of the vega value of forward-starting Asian call option between constant and stochastic volatility…………………………….94
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