請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/24160完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 呂育道 | |
| dc.contributor.author | Chin-Hong Wang | en |
| dc.contributor.author | 王志鴻 | zh_TW |
| dc.date.accessioned | 2021-06-08T05:17:20Z | - |
| dc.date.copyright | 2006-01-06 | |
| dc.date.issued | 2003 | |
| dc.date.submitted | 2005-12-08 | |
| dc.identifier.citation | Bibliography
[1] Amemiya, T., 1985, Advanced Econometrics, Basil Blackwell, London, UK. [2] Babbs, S., 2000, “Binomial Valuation of Lookback Options,”Journal of Economic Dynamics and Control 24, 1499-1525. [3] Black, F., M. Scholes, 1973, The pricing of Options and Corportate Liabilities, Journal of Political Economy 81, 637-654. [4]Boyle, P.P., 1997, Options : A Monte Carlo approach,”Journal of Fincial Economics 4, 323-338. [5] Boyle, P.P.,M. Broadie, and P.Glasserman.,1997,”Monte Carlo Methods for Security Pricing.”Journal of Economic Dynamics and Control,21, 8-9, 1267-1321. [6] Broadie, M. and P. Glasserman, 1997b, “pricing American-Style Securities Using Simulation,”Journal of Economic Dynamics and Control, 21, 1323-1352. [7] Broadie, M., P. Glasserman, and G. Jain, 1997, “Enhanced Monte Carlo Estimates for American Option Prices, “ Journal of Derivatives, 5,25-44. [8] Chen, I.-Y., T.-S. Dai, Y.-Y. Fang, and Y.-D. Lyuu, 2002, “Analytic Formula and Algorithm for Geometric-Average-Triger Reset Options,”Working Paper, Department of Computer Science and Information Engineering, National Taiwan University. [9] Cox, J., S. Ross, and M. Rubinstein, 1979, “Option Pricing : A simplified Approach,”Journal of Financial Economics 7, 229-264. [10] Dai, T.-S., and Y.-D. Lyuu, 2002, “Efficient, Exact Algorithms for Asian Options with Multiresolution Lattices,” To Appear in Proc. APFA/PACAP/FMA Finace Conference, Tokyo, July 14-17, 2002. [11] Dai, T.-S., 1999,”Pricing Path-Dependent Derivatives,”Master’s Thesis, Department of Computer Science and Information Engineering, National Taiwan University. [12] Hull, J., 2000, Options, Futures, and Other Derivatives, 4th ed., Englewood Cliffs, NJ: Prentice-Hall. [13] Hull J., and A. While, 1993,”Efficient Procedures for Valuing European and American Path-Dependence Options,”Journal of Derivatives 1, 21-31. [14] Harrison, J.M., and D.M. Dreps, 1979, “Martingales and Arbitrage in Multiperiod Securities Markets,”Journal of Economic Theory 20, 381-408. [15] Harrison, J.M., and S. R. Pliska, 1981, “Martingales and Stochastic Integrals in the Theory of continuous Trading,”Stochastic Processes and Their Applications 11, 261-271. [16] L. Stentoft, 2001, “Assessing the Least Squares Monte-Carlo Approach to American Option Valuation,” Working Paper, Centre for Analystical Finance, University of Aarhus-Aarhus School of Business. [17] Longstaff, F., and E. Schwartz, 2001, “Valuing American Options by simulation : A Simple Least-Squares Approach,”The Review of financial Studies, 14, 113-147. [18] Lyuu, Y.-D. 2002, Financial Engineering and Computation : Principles, Mathematics, and Algorithms, Cambridge, U.K. : Cambridge University Press. [19] Merton, R. C., 1973, “The Theory of Rational Option Pricing,” Bell Journal of Economics and Management Science 4, 141-183. [20] Royden, H.L., 1968, Real Analysis, MacMilllan, New York. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/24160 | - |
| dc.description.abstract | 中文摘要
本篇論文是使用Longstaff和Schwartz(2001)所發展之蒙地卡羅最小平方法(Least-Square Monte-Carlo simulation approach, LSM)來估計美移動平均選擇權之價值。蒙地卡羅模擬法以往無法解決美式選擇權提前履約的問題，因不知模擬出來的股價路徑最佳履約時點，而Longstaff和Schwartz提出的LSM演算法剛好可以有效選出每股價路徑的最佳履約點，解決蒙地卡羅評價美式選擇權的問題。 以美式賣權為例，LSM是利用蒙地卡羅法模擬一段期間每日(j)股票價格(Xj)之可能路徑,再依據選擇權契約所訂定的履約價格(K),算出每個股票價格路徑上每日之收益(Payoff，Max(Xj－K, 0))。然後從到期日開始，以到期日之全部股價路徑之收益诙因變項值，以到期昨日之股價為自變項值，做最小平方法簡單迴歸，求出β0、β1之(ｘj-1, E(Yj｜X=ｘj-1))簡單迴歸線的截距和斜率。再求出因變項平均值作為與當日收益價值作比較，若收益大於因變項平均值，則履約；反之，則不履約。再推往至前一日，重覆上述步驟，若每一條股價路徑有提前履約，則提前履約，直到契約成立日。再將每一條股價路徑中的最佳約日的收益，折現到契約成立日再進行算術平均，即可估算出美式賣權的價值 由於現今金融商品不斷創新，且日益複雜。而蒙地卡羅模擬法可價移動平均選擇權。但要評價美式移動平圴選擇權，須取前期股價，和移動平均珼做自變項變數，且為了讓消弭相關性，用Laguerre Polynomial模型使變數間彼此成正交。為了求證LSM演算法估計的準確性，用Dai(1999)的AuxiliaryState Variables和Ritchken & Trevor(1999)改良CRR Tree模丑來評價美式移動平均選擇權，結果可發現LSM和CRR所估計出來的值，差異都非常小。可觀察到LSM演算法實在非常強，可以評價如此複雜的金融商品。 本篇論文亦在以美式移動平均選擇權評價為例，進行探討如仃使LSM演算法估計更為準確。分為兩個部分，一個是迴歸自變項變數個數選取，另一是如何選擇較佳的自變數模型。在自變項變數個數選取上，至K = 2時，就非常準確，與K = 3所估計的值幾乎無差異。在選擇自變數模型上，比較了Monomials和Laguerre Polynomials，發現沒有做正交處理的Monomials模型，其估計出來的值和CRR與用Laguerre Polynomials做正交處理的LSM估計值，幾乎也無差異，這是一個較特別和驚訝的發現。若這發現是正確的，則用LSM演算法評價複雜式金融商品，都不用再對自變項變數間做正交處理了。 | zh_TW |
| dc.description.provenance | Made available in DSpace on 2021-06-08T05:17:20Z (GMT). No. of bitstreams: 1 ntu-92-R89723064-1.pdf: 249479 bytes, checksum: 98c0aeb0264889b722ce97e32816b7e6 (MD5) Previous issue date: 2003 | en |
| dc.description.tableofcontents | Content
1 Introduction 3 2 Preliminaries on Options Pricing 5 2.1 Simulation and option pricing………………………………………………5 2.1.1 Simulation from a Geometric Brownian Motion………………………5 2.1.2 Pricing European Options using simulation…………………………...6 2.1.3 Pricing American options using simulation……………………………6 2.2 Tree Models and Auxiliary State Variables…………………………………7 2.2.1 The CRR model………………………………………………………..8 2.2.2 Auxiliary State Variables………………………………………………9 3 The LSM Valuation Algorithm 10 3.1 The LSM valuation framework……………………………………………10 3.2 The LSM algorithm…………………………………………………….....11 3.3 The LSM algorithm to pricing American option………………………….12 3.3.1 The presentation of pricing American call options…………………...12 3.4 Convergence results ………………………………………………………14 4 Pricing Moving-Average-Lookback Options 16 4.1 Definition the AMVALs…………………………………………………..16 4.2 Pricing American-Style AMVALs………………………………………...17 4.2.1 The LSM methods……………………………………………………17 4.2.2 The CRR models……………………………………………………..18 4.3 Numerical Results…………………………………………………………19 4.3.1 Case1：Stock Price v.s. Volatility……………………………………19 4.3.2 Case2：Stock Price v.s. LB…………………………………………..20 4.3.3 Case3：Dividend Rate v.s. Reset Date……………………………….21 4.3.4 Case4：Reset Rate v.s. Different Reset Condition…………………...22 4.3.5 Case5：Moving –Average Number v.s. Volatility……………………23 4.3.6 Summary……………………………………………………………...24 5 What to Choose the Robustness of LSM? 25 5.1 Altering the number of regressors………………………………………...25 5.2 Using alternative polynomial families……………………………………26 6 Conclusions 28 Bibliography 29 | |
| dc.language.iso | en | |
| dc.subject | 蒙地卡羅 | zh_TW |
| dc.subject | 美式選擇權 | zh_TW |
| dc.subject | 評價 | zh_TW |
| dc.subject | 最小平方法 | zh_TW |
| dc.subject | Pricing American-Style | en |
| dc.subject | Monte Carlo Simulation | en |
| dc.subject | Least Square | en |
| dc.subject | Options | en |
| dc.title | 用蒙地卡羅最小平方法評價美式移動平均選擇權 | zh_TW |
| dc.title | Pricing American-Style Moving-Average Options with Least-Square Monte-Carlo Simulation Approaches | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 94-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 呂及人,徐讚昇 | |
| dc.subject.keyword | 蒙地卡羅,最小平方法,評價,美式選擇權, | zh_TW |
| dc.subject.keyword | Pricing American-Style,Options,Least Square,Monte Carlo Simulation, | en |
| dc.relation.page | 30 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2005-12-12 | |
| dc.contributor.author-college | 管理學院 | zh_TW |
| dc.contributor.author-dept | 財務金融學研究所 | zh_TW |
| 顯示於系所單位： | 財務金融學系 | |
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|---|---|---|---|
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