請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/26073完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 呂育道(Yuh-Dauh Lyuu) | |
| dc.contributor.author | Che-Chia Yu | en |
| dc.contributor.author | 游哲嘉 | zh_TW |
| dc.date.accessioned | 2021-06-08T06:59:38Z | - |
| dc.date.copyright | 2009-06-30 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-06-25 | |
| dc.identifier.citation | [1] Ait-Sahlia, F., Imhof, H., and Lai, T.-L. (2004) Pricing and Hedging of American Knock-in Options. Journal of Derivatives, Vol. 11, pp. 44–51.
[2] Andricopoulos, A.D., Widdicks, M., Duck, P.W., and Newton, D.P. (2003) Universal Option Valuation Using Quadrature Methods. Journal of Financial Economics, Vol. 67, pp. 447–471. [3] Beaglehole, D.R., Dybvig, P.H., and Zhou, G. (1997) Going to Extremes: Correcting Simulation Bias in Exotic Option Valuation. Financial Analyst Journal, Vol. 53, No. 1, pp. 62–68. [4] Black, F., and Scholes, M. (1973) The Pricing of Options and Corporate Liabilities. Journal of Political Economy, Vol. 81, pp. 637–659. [5] Boyle, P.P. (1977) Options: A Monte Carlo Approach. Journal of Financial Economics, No. 4, pp.323–338. [6] Boyle, P.P., and Lau, S.-H. (1994) Bumping Up against the Barrier with the Binomial Method. Journal of Derivatives, Vol. 2, pp. 6–14. [7] Chang, L.-B., and Palmer, K. (2007) Smooth Convergence in the Binomial Model. Finance and Stochastics, Vol. 11, No. 1, pp. 91–105. [8] Cheuk, T.H.F., and Vorst, T.C.F. (1996) Complex Barrier Options. Journal of Derivatives, Vol. 4, No. 1, pp. 8–22. [9] Cheuk, T.H.F., and Vorst, T.C.F. (1997) Currency Lookback Options and Observation Frequency: A Binomial Approach. Journal of International Money and Finance, Vol. 16, pp. 313–351. [10] Chung, S.-L., amd Shih, P.-T. (2007) Generalized Cox-Ross-Rubinstein Binomial Models. Management Science, Vol. 53, pp. 508–520. [11] Dai, T.-S., and Lyuu, Y.-D. (2008) The Bino-Trinomial Tree Model: A Simple Model for Efficient and Accurate Option Pricing. In Proceedings of the FMA European Conference, Prague, Czech. [12] Duffie, D. (1996) Dynamic Asset Pricing Theory. 2nd Edition. Princeton, NJ: Princeton University Press. [13] Duffy, Daniel J. (2006) Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach. 1st Edition. Chippenham, U.K.: John Wiley & Sons. [14] Faires, J.D., and Burden, R. (1998) Numerical Methods. 2nd Edition. Pacific Grove, CA: Brooks/Cole. [15] Figlewski, S., and Gao, B. (1999) The Adaptive Mesh Model: A New Approach to Efficient Option Pricing. Journal of Financial Economics, Vol. 53, pp. 313–351. [16] Haug, Espen Gaardner (1997) The Complete Guide to Option Pricing Formulas. 2nd Edition. New York, NY: McGraw-Hill. [17] Hsu, C.-Y. (2005) Adaptive Finite Volume Methods for Pricing European-Style Asian Options. Master's Thesis. Department of Computer Science and Information Engineering, National Taiwan University, Taiwan. [18] Hull, J.C. (2003) Options, Futures, and Other Derivatives. 5th Edition. Englewood Cliffs, NJ: Prentice Hall. [19] Liu, C.-C. (2000) Adaptive Finite-Volume Method for Solidification Problems. Master's Thesis. Department of Chemical Engineering, National Taiwan University, Taiwan. [20] Lyuu, Y.-D. (1998) Very Fast Algorithms for Barrier Option Pricing and the Ballot Problem. Journal of Derivatives, Vol. 5, No. 3, pp. 68–79. [21] Lyuu, Y.-D. (2002) Financial Engineering and Computation: Principles, Mathematics, Algorithms. Cambridge, U.K.: Cambridge University Press. [22] Merton, R. (1973) Theory of Rational Option Pricing. Bell Journal of Economics and Management, Vol. 4, pp. 141–183. [23] Odabasioglu, A., Celik, M., and Pileggi, L.T. (1998) PRIMA. IEEE Transaction on Computer-Aided Design of Integrated Circuits and Systems, Vol. 17, No. 8, pp. 645–654. [24] Persson, J. (2007) Pricing American Options Using a Space-Time Adaptive Finite Difference Method. Report 2008-004, Department of Information Technology, Uppsala University, Sweden. [25] Persson, J., and Sydow, L. von (2003) Pricing European Multi-Asset Options Using a Space-Time Adaptive FD-Method. Report 2003-059, Department of Information Technology, Uppsala University, Sweden. [26] Ritchken, P. (1995) On Pricing Barrier Options. Journal of Derivatives, Vol. 3, No. 2, pp. 19–28. [27] Shevchenko, P. (2003) Addressing the Bias in Monte Carlo Pricing of Multi-Asset Options with Multiple Barriers through Discrete Sampling. Journal of Computational Finance, Vol. 6, No. 3, pp. 1–20. [28] Tian, Y. (1999) A Flexible Binomial Option Pricing Model. Journal of Futures Markets, Vol. 19, No. 7, pp. 817–843. [29] Wang, F., and White, J. (1998) Automatic Model Order Reduction of a Microdevice Using the Arnoldi Approach. ASME IMECE, Vol. 66, pp. 527–530. [30] Widdicks, M., Andricopoulos, A.D., Newton, D.P., and Duck, P.W. (2002) On the Enhanced Convergence of Lattice Methods for Option Pricing. Journal of Futures Markets, Vol. 22, No. 4, pp. 315–338. [31] Yang, Y.-J., and Yu, C.-C. (2004) Extraction of Heat-Transfer Macromodels for MEMS Devices. Journal of Micromechanics and Microengineering, Vol. 14, pp. 587–596. [32] Zvan, R., Vetzal, K.R., and Forsyth, P.A. (1999) PDE Methods for Pricing Barrier Options. Journal of Economic Dynamics & Control, Vol. 24, pp. 1563–1590. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/26073 | - |
| dc.description.abstract | 本篇論文提出一個利用適應性精簡模型來評價障礙選擇權的方法。論文內容分為兩個部分：第一部份建立適應性有限差分法，第二部分則建立精簡模型。在適應性有限差分法中，我們發現雖然切割點數較少，但是計算出的結果仍較點數較多的均勻切割模型的誤差為小。在建立好適應性有限差分法後，我們利用Arnoldi演算法將原來適應式有限差分法的系統矩陣縮減成為小矩陣，藉以再進一步增加計算速度。實驗結果顯示，適應性有限差分法的結果在相同的切割點數上的誤差較Ritchken及adaptive mesh model的誤差為小。而適應性精簡模型的計算速度較未精簡前的適應性有限差分法為快。 | zh_TW |
| dc.description.abstract | This thesis presents an adaptive finite-difference method (FDM) with the model order reduction (MOR) technique for pricing vanilla European options and barrier options. We demonstrate that the adaptive FDM results agree with the closed-form results. Although the adaptive FDM uses fewer adaptive grid points than the equidistant FDM does, the absolute error of the adaptive FDM is lower than that of the equidistant FDM. The adaptive grid points generating process can be implemented as an automated process. We then show that the system matrices created by the adaptive FDM can be further reduced to low-order matrices by an Arnoldi-based model order reduction technique. We demonstrate that the numerical results by the adaptive MOR FDM for vanilla European options and barrier options again agree with the closed-form results. The computation time of the adaptive MOR FDM is significantly lower than that of the adaptive FDM. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T06:59:38Z (GMT). No. of bitstreams: 1 ntu-98-R94723081-1.pdf: 343512 bytes, checksum: 3b76ae0d03f3d96a2ca303a1269e05c9 (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | 口試委員會審定書..........................................#
誌謝......................................................i 中文摘要.................................................ii ABSTRACT................................................iii TABLE OF CONTENTS........................................iv LIST OF FIGURES..........................................vi LIST OF TABLES.........................................viii Chapter 1 Introduction....................................1 1.1 Introduction.....................................1 2.2 Organization of This Thesis......................5 Chapter 2 Option Basis....................................6 2.1 European Options.................................6 2.2 Barrier Options..................................7 Chapter 3 Theory.........................................10 3.1 Finite-Difference Methods.......................10 3.1.1 Finite-Difference Discretization................10 3.1.2 Boundary Conditions.............................11 3.2 Adaptive Grid Generation Method.................12 3.3 Methodology of the Model Order Reduction........14 Chapter 4 Experimental Results...........................17 4.1 Performance of the Adaptive FDM.................17 4.1.1 Single-Barrier Options..........................17 4.1.2 The Barrier-Too-Close Problem...................22 4.2 Performance of the Adaptive MOR FDM.............25 4.2.1 European Options................................25 4.2.2 Barrier Options.................................30 Chapter 5 Conclusion.....................................35 BIBLIOGRAPHY.............................................36 | |
| dc.language.iso | en | |
| dc.subject | 障礙選擇權 | zh_TW |
| dc.subject | 有限差分法 | zh_TW |
| dc.subject | 數值方法 | zh_TW |
| dc.subject | 精簡模型 | zh_TW |
| dc.subject | 適應性有限差分法 | zh_TW |
| dc.subject | Adaptive finite-difference method | en |
| dc.subject | Model order reduction | en |
| dc.subject | European options | en |
| dc.subject | Barrier options | en |
| dc.subject | Finite-difference method | en |
| dc.title | 以適應性有限差分精簡模型法評價障礙選擇權 | zh_TW |
| dc.title | Pricing Barrier Options by Adaptive Finite-Difference Methods with Model Order Reduction Techniques | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 97-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 戴天時(Tian-Shyr Dai),金國興(Kuo-Xing Jin) | |
| dc.subject.keyword | 有限差分法,障礙選擇權,數值方法,精簡模型,適應性有限差分法, | zh_TW |
| dc.subject.keyword | Adaptive finite-difference method,Finite-difference method,Barrier options,European options,Model order reduction, | en |
| dc.relation.page | 39 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2009-06-26 | |
| 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 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-98-1.pdf 未授權公開取用 | 335.46 kB | Adobe PDF |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。