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研究生:孫立憲
研究生(外文):Li-Hsien Sun
論文名稱:美式選擇權定價調整法-利用拔靴法
論文名稱(外文):Adjusted Methods for Pricing American Options Using Bootstrap
指導教授:鄭光甫鄭光甫引用關係
指導教授(外文):Kuang-Fu Cheng
學位類別:碩士
校院名稱:國立中央大學
系所名稱:統計研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
畢業學年度:93
語文別:英文
論文頁數:35
中文關鍵詞: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
外文關鍵詞:bootstrap methodAmerican optionsMarkov propertyStopping timesMartingalesLocal polynomial methodSimple linear regression
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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。
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 .
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
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.
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