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題名 卜瓦松指標下分支過程的股票定價模型及其應用
Stock pricing by Poisson indexed branching process and its application
作者 葉佳明
Ye, Jia-Ming
貢獻者 洪芷漪
Hong, Jyy-I
葉佳明
Ye, Jia-Ming
關鍵詞 股票價格
亞式選擇權
卜瓦松指標下分支過程
參數
估計量
定價公式
Stock price
Asian option
Poisson randomly indexed branching process
Estimator
Parameter
Pricing formula
日期 2022
上傳時間 2-Sep-2022 15:04:24 (UTC+8)
摘要 在風險中立市場上，我們以離散模型的角度去探討選擇權
，在本論文我們沿續Epps(1996)以 Poisson randomly indexed branching process 來定價股票價格，並且提出更佳的估計參數方法，同時給出亞式選擇權的定價模型。
In a risk-neutral market, we explore options from the perspective of a discrete model.
In this thesis, we follow Epps` (1996) for price stock using the Poisson randomly indexed branching process and propose an estimation for the parameters. Moreover, we also apply this model to provide a pricing formula for the Asian Option.
參考文獻 Bibliography
[1] K.B. Athreya and P.E. Ney. Branching Processes. Grundlehren der mathematischen Wissenschaften. Springer Berlin Heidelberg, 1972.
[2] Jean-Pierre Dion and Belkheir Essebbar. On the statistics of controlled branching processes.
In Branching processes, pages 14–21. Springer, 1995.
[3] JP Dion and TW Epps. Stock prices as branching processes in random environments: estimation. Communications in Statistics-Simulation and Computation, 28(4):957–975, 1999.
[4] JP Dion and WW Esty. Estimation problems in branching processes with random environments. The Annals of Statistics, pages 680–685, 1979.
[5] TW Epps. Stock prices as branching processes. Stochastic Models, 12(4):529–558, 1996.
[6] Theodore Edward Harris et al. The theory of branching processes, volume 6. Springer Berlin, 1963.
[7] Georgi Mitov and Kosto Mitov. Option pricing by branching process. Pliska Studia Mathematica Bulgarica, 18(1):213p–224p, 2007.
[8] S James Press. A compound events model for security prices. Journal of business, pages 317–335, 1967.
[9] NM Yanev. Limit-theorems for estimators in galton-watson branching-processes. DOKLADI NA BOLGARSKATA AKADEMIYA NA NAUKITE, 38(6):683–686, 1985.
描述 碩士
國立政治大學
應用數學系
107751009
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0107751009
資料類型 thesis
dc.contributor.advisor 洪芷漪zh_TW
dc.contributor.advisor Hong, Jyy-Ien_US
dc.contributor.author (Authors) 葉佳明zh_TW
dc.contributor.author (Authors) Ye, Jia-Mingen_US
dc.creator (作者) 葉佳明zh_TW
dc.creator (作者) Ye, Jia-Mingen_US
dc.date (日期) 2022en_US
dc.date.accessioned 2-Sep-2022 15:04:24 (UTC+8)-
dc.date.available 2-Sep-2022 15:04:24 (UTC+8)-
dc.date.issued (上傳時間) 2-Sep-2022 15:04:24 (UTC+8)-
dc.identifier (Other Identifiers) G0107751009en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/141636-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學系zh_TW
dc.description (描述) 107751009zh_TW
dc.description.abstract (摘要) 在風險中立市場上，我們以離散模型的角度去探討選擇權
，在本論文我們沿續Epps(1996)以 Poisson randomly indexed branching process 來定價股票價格，並且提出更佳的估計參數方法，同時給出亞式選擇權的定價模型。		zh_TW
dc.description.abstract (摘要) In a risk-neutral market, we explore options from the perspective of a discrete model.
In this thesis, we follow Epps` (1996) for price stock using the Poisson randomly indexed branching process and propose an estimation for the parameters. Moreover, we also apply this model to provide a pricing formula for the Asian Option.		en_US
dc.description.tableofcontents Contents
致謝 i
中文摘要 ii
Abstract iii
Contents iv
1 Model Setting 1
1.1 Branching process 1
1.1.1 Some classic results 3
1.1.2 An example of branching process with geometric offspring distribution 4
1.2 Poisson randomly indexed branching process . . . . . . . . . . . . . . . . . . 9
1.3 Stock pricing formula by Epps . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 Estimation of Parameters 15
2.1 Limit distribution of the normalized price changes . . . . . . . . . . . . . . . . 16
2.2 Epps’ estimations of parameters . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 Revised estimation of parameter . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 Numerical comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4.1 Estimation for λ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4.2 Estimation for σ^2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4.3 Estimation for m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3 Application to Asian Put Option 29
3.1 The risk-neutral probability measure Q . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Pricing formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4 Conclusions 40
Bibliography 42		zh_TW
dc.format.extent 638509 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0107751009en_US
dc.subject (關鍵詞) 股票價格zh_TW
dc.subject (關鍵詞) 亞式選擇權zh_TW
dc.subject (關鍵詞) 卜瓦松指標下分支過程zh_TW
dc.subject (關鍵詞) 參數zh_TW
dc.subject (關鍵詞) 估計量zh_TW
dc.subject (關鍵詞) 定價公式zh_TW
dc.subject (關鍵詞) Stock priceen_US
dc.subject (關鍵詞) Asian optionen_US
dc.subject (關鍵詞) Poisson randomly indexed branching processen_US
dc.subject (關鍵詞) Estimatoren_US
dc.subject (關鍵詞) Parameteren_US
dc.subject (關鍵詞) Pricing formulaen_US
dc.title (題名) 卜瓦松指標下分支過程的股票定價模型及其應用zh_TW
dc.title (題名) Stock pricing by Poisson indexed branching process and its applicationen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Bibliography
[1] K.B. Athreya and P.E. Ney. Branching Processes. Grundlehren der mathematischen Wissenschaften. Springer Berlin Heidelberg, 1972.
[2] Jean-Pierre Dion and Belkheir Essebbar. On the statistics of controlled branching processes.
In Branching processes, pages 14–21. Springer, 1995.
[3] JP Dion and TW Epps. Stock prices as branching processes in random environments: estimation. Communications in Statistics-Simulation and Computation, 28(4):957–975, 1999.
[4] JP Dion and WW Esty. Estimation problems in branching processes with random environments. The Annals of Statistics, pages 680–685, 1979.
[5] TW Epps. Stock prices as branching processes. Stochastic Models, 12(4):529–558, 1996.
[6] Theodore Edward Harris et al. The theory of branching processes, volume 6. Springer Berlin, 1963.
[7] Georgi Mitov and Kosto Mitov. Option pricing by branching process. Pliska Studia Mathematica Bulgarica, 18(1):213p–224p, 2007.
[8] S James Press. A compound events model for security prices. Journal of business, pages 317–335, 1967.
[9] NM Yanev. Limit-theorems for estimators in galton-watson branching-processes. DOKLADI NA BOLGARSKATA AKADEMIYA NA NAUKITE, 38(6):683–686, 1985.		zh_TW
dc.identifier.doi (DOI) 10.6814/NCCU202201402en_US