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| 研究生： |
葉佳明 Ye, Jia-Ming |
|---|---|
| 論文名稱： |
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 |
| 指導教授： |
洪芷漪
Hong, Jyy-I |
| 口試委員: |
陳隆奇
Chen, Lung-Chi 孫立憲 Sun, Li-Hsien |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 2022 |
| 畢業學年度： | 110 |
| 語文別： | 英文 |
| 論文頁數： | 42 |
| 中文關鍵詞： | 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 |
| 外文關鍵詞： | Stock price, Asian option, Poisson randomly indexed branching process, Estimator, Parameter, Pricing formula |
| DOI URL： | http://doi.org/10.6814/NCCU202201402 |
| 相關次數： | 點閱：193 下載：24 |
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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.
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
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[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.
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[9] NM Yanev. Limit-theorems for estimators in galton-watson branching-processes. DOKLADI NA BOLGARSKATA AKADEMIYA NA NAUKITE, 38(6):683–686, 1985.
