政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/141636

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/141636

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政大典藏 > College of Science > Department of Mathematical Sciences > Theses > Item 140.119/141636

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/141636

Title:	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
Authors:	葉佳明 Ye, Jia-Ming
Contributors:	洪芷漪 Hong, Jyy-I 葉佳明 Ye, Jia-Ming
Keywords:	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
Date:	2022
Issue Date:	2022-09-02 15:04:24 (UTC+8)
Abstract:	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.
Reference:	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.
Description:	碩士國立政治大學應用數學系 107751009
Source URI:	http://thesis.lib.nccu.edu.tw/record/#G0107751009
Data Type:	thesis
DOI:	10.6814/NCCU202201402
Appears in Collections:	[Department of Mathematical Sciences] Theses

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