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姓名 孫立憲(Li-Hsien Sun) 查詢紙本館藏 畢業系所 統計研究所 論文名稱 美式選擇權定價調整法-利用拔靴法
(Adjusted Methods for Pricing American Options Using Bootstrap)相關論文 檔案 [Endnote RIS 格式]
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摘要(中) 在本文中，我們介紹如何使用模擬的方法來估算可及早履約選擇權的價值。首先，我們說明如何在任意一個有限並且是離散時間的馬可夫過程(Markovian process)中去計算它的最佳停止時間。接著，去利用條件期望值來估計最佳停止時間。而在馬可夫過程的假設下，迴歸模型可以用來幫助我們估計條件期望值。在這裡，我們介紹了兩種方法：局部線性迴歸(Local linear regression)和簡單線性迴歸。最後，則是運用拔靴法(Bootstrap method)和局部線性迴歸在未知波動的情況下來調整我們的估計。 摘要(英) In this thesis, we show how to value the early exercise options with simulation. Above all, we present how to value the optimal stopping time for any Markovian process in finite discrete time and the estimation of decision rule to early exercise by conditional expectation. For Markovian process, the conditional expectation can be estimated with regression models. Local polynomial kernel estimators and simple linear regression are used in our experiments. After that, we apply bootstrap method and local polynomial kernel method to adjust our estimate without knowing the real volatility . 關鍵字(中) ★ 美式選擇權
★ 馬可夫過程
★ 最佳停止時間
★ 平賭過程(Martingale)
★ 簡單線性迴歸
★ 局部線性迴歸
★ 拔靴法關鍵字(英) ★ bootstrap method
★ American options
★ Markov property
★ Stopping times
★ Martingales
★ Local polynomial method
★ Simple linear regression論文目次 Contents
1.Introduction...........................1
2.Description of Theory..................3
2.1 The Intrinsic Value of an Option....3
2.2 The Optimal Stopping Time...........4
2.3 Valuation of European Options.......6
2.4 Valuation of American Call Option...7
2.5 The Approximation Algorithm of the Early Exercise Options.........................8
3.Regression Model......................10
3.1 Local Polynomial Kernel Estimators.10
3.2 Simple Linear Regression...........16
3.3 Approximating the Value of an American Put Option..................................18
3.4 Properties of the Estimator....19
4.Improve Estimation by Bootstrap Method23
4.1 Taylor Series......................23
4.2 Bootstrap Method...................24
4.3 Approximating the Value of American Put Option by Bootstrapping.................25
4.4 Comparison of Estimators...........26
4.5 Properties of Estimators...........27
5.Conclusion............................32
Reference...............................33參考文獻 Reference
1.Andre, I. Khuri, 1993, “Advanced Calculus with Applications in
Statistics,” 108-112.
2.Carriere, J., 1996, “Valuation of Early-Exercise Price of options Using
Simulations and Nonparametric Regression,” Insurance: Mathematics and
Economics, 19, 19-30.
3.Chow, Y.S., H. Robbins and D. Siegmund, 1971, Great Expectations: The Theory
of Optimal stopping. Houghton Mifflin, New York, NY.
4.Davison, A. C. and Hinkley, D. V., 1997, “Bootstrap Methods and Their
Application,” Cambridge University Press.
5.Efron, B., 1979a, “Bootstrap Methods: Another Look at the Jackknife,
Insurance: Annals of Statistics, 7, 1-26.
6.Longstaff, F. and Schwartz, E., 2001, “Valuing American Options by
Simulation: A Simple Least-Square Approach,” Insurance: The Review of
Financial Studies Spring 2001 Vol. 14, No. 1, 113-147.
7.Schimek, Michael G.,“Smoothing and Regression,” 229-276.
8.Ross, Sheldon M. “Introduction to Probability Models,” Eighth edition, 350.
9.Ross, Sheldon M “Simulations,” Third Edition, 118-124.
10.Tiley, J.A., 1993, “Valuing American options in a path simulation model,”
Insurance: Transaction, Vol. XLV. Society of Actuaries, Schaumburg, 499-549.指導教授 鄭光甫(Kuang-Fu Cheng) 審核日期 2005-7-6 推文 plurk
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