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研究生:何信慶
研究生(外文):Hsin-Ching Ho
論文名稱:智慧型計算於選擇權近似公式之研究
論文名稱(外文):Approximation Formulae of Option Pricing Using Computational Intelligence
指導教授:吳憲忠
指導教授(外文):Hsien-Chung Wu
學位類別:碩士
校院名稱:國立暨南國際大學
系所名稱:資訊管理學系
學門:電算機學門
學類:電算機一般學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:93
中文關鍵詞:選擇權基因規劃蟻群最佳化模擬退火法禁制搜尋法
外文關鍵詞:Option PricingGenetic ProgrammingAnt Colony OptimizationSimulated annealingTabu Search
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隨著時代的變遷與進步,衍生性金融商品也隨之熱絡起來。隨著這些新金融商品的興起,伴隨而來的便是定價的問題。本篇論文的目的便是要分析與研究智慧型計算(Computational Intelligence)在尋找選擇權(Option)近似公式上的可行性。在本研究中使用了四種常見的智慧型計算方法來尋找選擇權近似公式,這四種方法分別是基因規劃(Genetic Programming)、蟻群最佳化(Ant Colony Optimization)、模擬退火法(Simulated Annealing)和禁制搜尋法(Tabu Search)。
本研究將透過兩個構面指出這四種方法在尋找選擇權近似公式的可行性,第一個構面是比較方法的正確性,也就是說比較這四種方法所找出來的最佳定價方程式在測試資料上的誤差大小。第二個構面是比較方法的效率,也就是說比較這四種方法在相同的時間內所找到的定價方程式在訓練資料上的誤差大小。
Owing to many of the analytic formulae for option prices can not be obtained, the purpose of this thesis is to obtain approximation formulae for option prices by using the computational intelligence. Four well-known searching techniques will be invoked in this thesis, that is, genetic programming、ant colony optimization、simulated annealing and tabu search.
There are two aspects to analyze the approximation formulae for option prices. The first aspect is to compare the accuracy of the approximation formulae obtained by those techniques. The idea is to evaluate the testing errors which are obtained by the optimal approximation formulae. The second aspect is to compare the efficiency of these techniques. The idea is to compare the training errors using the same running (CPU) time.
目錄
1緒論 9
1.1研究動機............................................. 9
1.2研究背景.............................................10
1.3研究目的.............................................10
1.4論文架構.............................................11
1.5研究方法與限制.......................................12
2相關理論介紹 14
2.1選擇權(Option)定價模型...............................14
2.1.1何謂選擇權......................................14
2.1.2常見的選擇權價格影響因素........................15
2.1.3解析模型(Analytical Model)......................16
2.1.4數值分析法(Numerical Analysis Approach).........17
2.1.5解析近似模型(Analytic Approximation Model)......18
2.2剖析樹(Parse Tree)...................................18
2.3基因演算法(Genetic Algorithm)........................20
2.3.1基因規劃(Genetic Programming)...................21
2.4蟻群最佳化(Ant Colony Optimization)..................23
2.4.1蟲群智慧(Swarm Intelligence)....................24
2.5模擬退火法(Simulated Annealing)......................26
2.5.1默察波利斯演算法(Metropolis Algorithm)..........27
2.6禁制搜尋法(Tabu Search)..............................29
3相關文獻探討 32
3.1基因規劃(Genetic Programming)在選擇權上的應用........32
3.2蟻群最佳化(Ant Colony Optimization)在選擇權上的應用..32
3.3分析討論.............................................37
3.3.1注意事項........................................37
3.3.2重點分析........................................38
3.3.3分析比較........................................39
4智慧型計算(Computational Intelligence)之演算法規劃 41
4.1剖析樹(Parse Tree)的建立與編碼.......................42
4.2基因規劃(Genetic Programming)........................45
4.2.1適合度函數(Fitness Function)....................45
4.2.2重製(Reproduction)..............................46
4.2.3交配(Crossover).................................47
4.2.4突變(Mutation)..................................47
4.2.5策略應用與參數設定..............................47
4.3蟻群最佳化(Ant Colony Optimization)..................49
4.3.1完整的剖析樹(Parse Tree)........................49
4.3.2狀態轉移規則(State Transition Rule).............51
4.3.3費洛蒙(Pheromone)更新...........................52
4.3.4策略應用與參數設定..............................52
4.4模擬退火法(Simulated Annealing)......................53
4.4.1尋找鄰居的方法..................................53
4.4.2策略應用與參數設定..............................56
4.5禁制搜尋法(Tabu Search)..............................56
4.5.1禁制的準則......................................56
4.5.2策略應用與參數設定..............................57
5實驗與討論 58
5.1美式賣權(American Put Option)........................58
5.1.1變數的選擇......................................58
5.1.2參數的調整......................................59
5.1.3實驗結果........................................66
5.2歐式買權(European Call Option).......................69
5.2.1變數的選擇......................................69
5.2.2參數的調整......................................70
5.2.3實驗結果........................................76
6結論與未來展望 79
6.1結論.................................................79
6.2未來展望.............................................80
參考文獻 81
附錄 84
A基因規劃所得到的方程式 84
A.1美式賣權.............................................84
A.2歐式買權.............................................85
B蟻群最佳化所得到的方程式 86
A.1美式賣權.............................................86
A.2歐式買權.............................................87
A模擬退火法所得到的方程式 88
A.1美式賣權.............................................88
A.2歐式買權.............................................89
A禁制搜尋法所得到的方程式 92
A.1美式賣權.............................................92
A.2歐式買權.............................................93
圖目錄
1.1研究流程圖..............................................12
2.1剖析樹y=b+a*x...........................................20
2.2基因演算法流程圖........................................23
2.3蟻群最佳化流程圖........................................25
2.4模擬退火法演算法流程圖..................................28
2.5禁制搜尋法流程圖........................................31
3.1權重尋找路徑示意圖......................................35
3.2程式語法圖..............................................36
4.1剖析樹b+a*x.............................................43
4.2二元樹b+a*x.............................................43
4.3子樹尋找示意圖..........................................44
4.4二元樹交配(Crossover)示意圖.............................48
4.5研究中所採用的蟻群最佳化流程圖..........................50
4.6螞蟻建樹示意圖..........................................51
4.7替代操作示意圖..........................................54
4.8修改操作示意圖..........................................55
5.1美式選擇權關鍵要素圖....................................59
5.2在相同突變率下,不同交配率的誤差比較長條圖..............60
5.3在相同交配率下,不同突變率的誤差比較長條圖..............61
5.4在相同費洛蒙殘留率下,不同蟻群數目的誤差比較長條圖......62
5.5在相同蟻群數目下,不同費洛蒙殘留率的誤差比較長條圖......62
5.6在相同初始溫度下,不同的初始馬可夫鍊長度之誤差比較長條圖63
5.7在相同初始馬可夫鍊長度下,不同初始溫度的誤差比較長條圖..64
5.8在相同禁制數目下,不同鄰居數目的誤差比較長條圖..........65
5.9在相同鄰居數目下,不同禁制數目的誤差比較長條圖..........65
5.10完整收斂速度比較圖.....................................66
5.11部份收斂速度比較圖.....................................67
5.12美式賣權完整誤差比較圖.................................68
5.13美式賣權部份誤差比較圖.................................69
5.14歐式選擇權關鍵要素圖...................................69
5.15在相同突變率下,不同交配率的誤差比較長條圖.............71
5.16在相同交配率下,不同突變率的誤差比較長條圖.............71
5.17在相同費洛蒙殘留率下,不同蟻群數目的誤差比較長條圖.....72
5.18在相同蟻群數目下,不同費洛蒙殘留率的誤差比較長條圖.....73
5.19在相同初始溫度下,不同的初始馬可夫鍊長度之誤差比較長條圖74
5.20在相同初始馬可夫鍊長度下,不同初始溫度的誤差比較長條圖.74
5.21在相同禁制數目下,不同鄰居數目的誤差比較長條圖.........75
5.22在相同鄰居數目下,不同禁制數目的誤差比較長條圖.........76
5.23收斂速度比較圖.........................................77
5.24歐式買權誤差比較圖.....................................78
表目錄
2.1選擇權(Option)的種類....................................15
2.2選擇權解析模型(Analytical Model)的族譜..................17
2.3選擇權數值分析法(Numerical Analysis Approach)的種類.....18
2.4選擇權解析近似模型(Analytic Approximation Model)........19
2.5簡單的程式語言(Programming Language)文法(Grammar)例子...19
2.6基因演算法(Genetic Algorithm)需規劃的主要項目...........22
2.7蟻群最佳化(Ant Colony Optimization)主要名詞介紹.........26
3.1美式與歐式選擇權所需變數、運算子與函數的比較............34
3.2運算權重分配表..........................................34
3.3費洛蒙(Pheromone)參考表.................................35
3.4智慧型計算演算法比較表..................................40
4.1本研究的通用文法(Grammar)...............................41
4.2本研究的運算權重表......................................44
4.3基因種類彙總表..........................................48
5.1基因規劃參數調整表......................................60
5.2蟻群最佳化參數調整表....................................61
5.3模擬退火法參數調整表....................................63
5.4禁制搜尋法參數調整表....................................64
5.5美式選擇權實驗誤差表....................................67
5.6基因規劃參數調整表......................................70
5.7蟻群最佳化參數調整表....................................72
5.8模擬退火法參數調整表....................................73
5.9禁制搜尋法參數調整表....................................75
5.10歐式選擇權實驗誤差表...................................67
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