隨機波動模型下參數之最大概似估計

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：16

、訪客IP：18.191.210.18

姓名

張家榮(Chia-jung Chang) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

隨機波動模型下參數之最大概似估計
(Maximum Likelihood Estimation of Parameterson the Stochastic Volatility Model)

相關論文

★ SABR模型下使用遠期及選擇權資料的參數估計	★ 台灣指數上的股價報酬預測性
★ 台灣股票在alpha-TEV frontier上的投資組合探討與推廣	★ On Jump Risk of Liquidation in Limit Order Book
★ 結構型商品之創新、評價與分析	★ 具有厚尾殘差下有效地可預測性檢定
★ A Dynamic Rebalancing Strategy for Portfolio Allocation	★ A Multivariate Markov Switching Model for Portfolio Optimization
★ 漸進最佳變點偵測在金融科技網路安全之分析	★ Reducing forecasting error under hidden markov model by recurrent neural networks
★ Empirical Evidences for Correlated Defaults	★ 金融市場結構轉換次數的偵測
★ 重點重覆抽樣下拔靴法估計風險值-以台泥華碩股票為例	★ 在DVEC-GARCH模型下風險值的計算與實證研究
★ 資產不對稱性波動參數的誤差估計與探討	★ 公司營運狀況與員工股票選擇權之關係

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

假如金融市場上的股價（stock）走勢跟隨Heston 模型，則
可以藉由股價資料來推估參數，而若引進選擇權（option）的資
料，來處理觀察不到的波動度，也可以由股價跟選擇權的資料推
估參數。在這篇論文裡我們有兩種方法去推估參數：方法一是只
有股價資料時，這時候假設波動度（volatility）是可以觀察到的；
方法二是當波動度是觀察不到時，我們選用選擇權資料利用轉換
來代替觀察不到的波動度去推估參數。因此我們想知道上述兩種
參數估計的差距。本文使用最大概似估計法（maximum likelihood
estimator, MLE）來驗證。也利用蒙地卡羅模擬以及有母數拔靴
(parametric bootstrap) 重複抽樣方法去比較兩者的結果是否一
致。

摘要(英)

In this paper, we want to know if the financial market stock
price trend to follow Heston model, we can estimate the parameters
by stock price data when the volatility is assumed to be observable,
and while the volatility does not observed, we can use option data to
deal with that, then use stock and option data to estimate the
parameters. In this paper, we have two methods to estimate the
parameters: one method only stock information, the assumption that
volatility is to be observed; method 2 is the assumption that
volatility is not observable, we use options data instead of using
conversion can not see the volatility to estimate the parameters. We
would like to know the difference between the estimation accuracy
of the theoretical exact value. In order to count the value of this
theory, we use the maximum likelihood estimator(MLE) to estimate
the parameters of the stochastic volatility model in the consistency
of MLE estimation. We also use the Monte Carlo simulation and the
papametric bootstrap method of repeated sampling to compare the
results.

關鍵字(中)

★ 有母數拔靴法
★ 蒙地卡羅模擬
★ Heston 模型
★ 波動度

關鍵字(英)

★ Heston model
★ volatility
★ Monte Carlo simulation

論文目次

摘要 ....................................................... i
英文摘要.................................................. ii
誌謝..................................................... iii
目錄...................................................... iv
表目錄..................................................... v
符號說明.................................................. vi
一、緒論................................................... 1
1.1 研究動機與目的................................... 1
1.2 論文架構概述..................................... 4
二、文獻回顧............................................... 5
2.1 模擬Heston 模型股價之介紹........................ 5
2.2 模擬Heston 模型選擇權價格之介紹.................. 7
三、參數估計之方法........................................ 10
3.1 可直接觀察波動度下，概似函數之介紹.............. 10
3.2 無法直接觀察波動度下，概似函數之介紹............ 12
四、Heston 模型參數估計之分析............................. 15
4.1 資料模擬及方法分析.............................. 15
五、結論.................................................. 25
參考文獻.................................................. 26
附錄...................................................... 27

參考文獻

[1] Ait-Sahalia, Y., 1999. Transition densities for interest rate and other nonlinear
diffusions. Journal of Finance.54, 1361-1395.
[2] Ait-Sahalia, Y., 2001. Closed-form likelihood expansions for multivariate
diffusions. Tech. rep., Princeton University.
[3] Ait-Sahalia, Y., 2002. Maximum-likelihood estimation of discretely sampled
diffusions: A closed-form approx-imation approach. Econometrica
70, 223-262.
[4] Ait-Sahalia, Y., Lo, A., 1998. Nonparametric estimation of state-pricedensities
implicit in financial asset prices. Journal of Finance 53, 499-
547.
[5] Ait-Sahalia, Y., Mykland, P. A., 2003. The effects of random and discrete
sampling when estimating continuous-time diffusions. Econometrica
71, 483-549.
[6] Andersen, T., Bollerslev, T., Meddahi, N., 2002a. Analytic evaluation
of volatility forecasts. Tech. rep., North-Western University.
[7] Andersen,T.G.,Benzoni,L.,Lund,J.,2002b.Anempirical investigation of
continuous-time equity return models. Journal of Finance 57, 1239-
1284.
[8] Bakshi, G., Cao, C., Chen, Z., 1997. Empirical performance of alternative
option pricing models. Journal of Finance 52, 2003-2049.
[9] Bates, D. S., 2000. Post-’87 crash fears in the S&P 500 futures option
market. Journal of Econometrics 94, 181-238.
[10] Bates, D. S., 2002. Maximum likelihood estimation of latent affine processes.
Tech. rep., University of Iowa.

指導教授

傅承德(Cheng-Der Fuh)

審核日期

2010-7-2

推文