請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/55667完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 韓傳祥 | |
| dc.contributor.author | Wei-Zhi Qin | en |
| dc.contributor.author | 秦唯植 | zh_TW |
| dc.date.accessioned | 2021-06-16T04:16:02Z | - |
| dc.date.available | 2019-08-25 | |
| dc.date.copyright | 2014-08-25 | |
| dc.date.issued | 2014 | |
| dc.date.submitted | 2014-08-20 | |
| dc.identifier.citation | [1] Beaulieu, N. C. and Rajwani, F. “Highly accurate simple closed-form approximationsto lognormal sum distributions and densities,” IEEE Communications Letters,vol. 8, no. 12, 709–711, 2004.
[2] Beaulieu, N. C. and Xie, Q. “An optimal lognormal approximation to lognormal sum distributions,” IEEE Transactions on Vehicular Technology, vol. 53, no. 2, 479–489,2004. [3] Curran, M. “Valuing Asian and Portfolio Options by Conditioning on the Geometric Mean Price.” Management Science, 40(12): 1705-1711. 1994 [4] Dhaene, J., Denuit, M., Goovaerts, M.J., Kaas, R. and Vyncke, D. “The concept Of comonotonicity in actuarial science and finance: theory.” Insurance: Mathematics& Economics, 31, 3-33 , 2002a. [5] Dhaene, J., Denuit, M., Goovaerts, M.J., Kaas, R. and Vyncke, D. “The concept of comonotonicity in actuarial science and finance: applications.” Insurance: Mathematics& Economics, 31, 133-161,2002b. [6] Deelstra, G., Diallo, I., Vanmaele, M. “Moment matching approximation of Asian basket option prices.” Journal of Computational and Applied Mathematics 234,1006–1016 , 2010. [7] Dingec, K. D. and Hormann, W. “Variance Reduction for Asian Options.” working paper. Bogazici University,2010. [8] Dingec, K. D. and Hormann, W. “Control variates and conditional Monte Carlo for basket and Asian options,” Insurance: Mathematics and Economics 52, 421–434,2013. [9] Deelstra, G., Liinev J. and Vanmaele M. “Pricing of arithmetic basket options by conditioning,” Insurance: Mathematics & Economics, 34, 55-57,2004. [10] Deelstra, G., Diallo I. and Vanmaele M. “Bounds for Asian basket options,” Journal of Computational and Applied Mathematics, 218,215-228,2008. [11] Gao, X., Xu, Hong and Ye, D. “Asymptotic Behaviour of Tail Density for Sum ofCorrelated Lognormal Variables.” International Journal of Mathematics and Mathematical Sciences. 2009: 1-28. [12] Guasoni, P. and Robertson, S. “Optimal Importance Sampling With Explicit Formulas In Continuous Time. Finance Stochastics.” 12, 1-19. 2008 Vectors. The Annals of Applied Probability. 19(5), 1687-1718. 2009 disciplines. Working paper, Moscow State University. [13] Han, C.-H. “Optimal Variance Minimization: A New Importance Sampling Methodby High-Dimensional Embedding.” working paper. [14] Homem-de-Mello. ”A Study on the Cross-Entropy Method for Rare-Event Probability Estimation,” INFORMS journal on Computing 19(3), 381-394. [15] Homen-de-Mello, T. and R.Y. Rubinstein. “Rare Event Estimation for static MOdels via Cross-Entropy and Importance Sampling.” ,2002. [16] Lam C.-L. J. and Le-Ngoc, T.”Estimation of typical sum of lognormal random variablesusing log shifted gamma approximation,”IEEE Communications Letters, vol.10, no. 4, 234–235, 2006. [17] Milevsky M. A. and S. E. Posner, ”Asian options, the sum of lognormals, and the reciprocal gamma distribution,” Journal of Financial and Quantitative Analysis, vol.33, no. 3, 409–422, 1998. [18] Kaas R., Dhaene J., and Goovaerts M.J. ”Upper and lower bounds for sums of random variables.” Insurance: Mathematics & Economics, 27, 151-168, 2000. [19] Kemna, A., Vorst, A. ”A pricing method for options based on average asset values.”Journal of Banking & Finance 14, 113–130,1990. [20] Wu,J. Mehta, N. B. and Zhang, J. “Flexible lognormal sum approximation method,”in Proceedings of IEEE Global Telecommunications Conference (GLOBECOM’05), vol. 6, 3413–3417, St. Louis, Mo,USA, December 2005. [21] Zhao L. and Ding, J. A strict approach to approximating lognormal sum distributions, in Proceedings of the Canadian Conference on Electrical and Computer Engineering(CCECE ’06), 916-919, Ottawa,Canada, May 2006. [22] Zhang, Q. T. and Song, S. H. ”Model selection and estimation for lognormal sumsin Pearson’s framework,” in Proceedings of the 63rd IEEE Vehicular Technology Conference (VTC ’06), vol. 6, 2823–2827,Melbourne,Australia, May 2006. [23] Bucklew,J.A. ”Introduction to Rare Event Simulation.” Springer-Verlag: New York. [24] Johnson, R. A. and D. W. Wichern, ”Applied Multivariate Statistical Analysis,”Prentice-Hall, Inc., NJ, 1982 [25] Stroock,D.W. ”Probability Theory, an Analytic View.” Cambridge University Press,Cambridge(2011) | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/55667 | - |
| dc.description.abstract | 在這篇文章，我們討論了控制變異法結合重要抽樣法在亞式選擇權定價下之應用，我們以 [7] 為基礎，提出數個更動重要抽樣法準則的估計方法。並提出一些理論架構，接下來，我們討論更動控制變異的一般方法。最後，我們討論此種方法在違約機率上的計算，以及上述方法的數值結果及討論。 | zh_TW |
| dc.description.abstract | We dicuss the Asian option pricing problem under the geometric Brown-ian motion assumption. Digec and Horrman [7] give a method based on the combination of conditional importance sampling and control variate method. First we revise the conditional important sampling part by using different im-portance sampling critique including efficient estimator and using some ap-proximation distribution. We give some theoretical support to our method. And then we give the numerical results of this revised method. Second we discuss the possibility of the control variate part to form a general method to deal with this problem. Finally we estimate the probability P ( ≥ ) and discuss the numerical result. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T04:16:02Z (GMT). No. of bitstreams: 1 ntu-103-R01221015-1.pdf: 2112979 bytes, checksum: 4eae5935c21417834f301bf6334319d0 (MD5) Previous issue date: 2014 | en |
| dc.description.tableofcontents | 委員審定書 i
Abstract ii 中文摘要iii Contents iv 1 Introduction 1 2 Preliminaries 4 2.1 Asian option pricing and naive simulation under Black-Sholes environment 4 2.2 Control variates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.1 The classical control variates for Asian option . . . . . . . . . . . 5 2.2.2 The new control variates for Asian option . . . . . . . . . . . . . 7 2.2.3 The additional control variate method . . . . . . . . . . . . . . . 8 2.3 Importance sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.1 Different Criterion of importance sampling . . . . . . . . . . . . 11 2.3.2 Cross entropy method . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 Approximation of sum of lognormal random variable . . . . . . . . . . . 14 3 Method formation 15 3.1 Review of Digence and Hormann’s Method . . . . . . . . . . . . . . . . 15 3.2 Efficient I.S approach . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.3 Variance minimum I.S approach . . . . . . . . . . . . . . . . . . . . . . 19 3.4 General conditional method . . . . . . . . . . . . . . . . . . . . . . . . . 23 4 The probability of {A C} 25 5 numerical results 27 5.1 Revised Importance Sampling results . . . . . . . . . . . . . . . . . . . 27 5.2 Default Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 6 Conclusion 35 7.Bibliography..................36 | |
| dc.language.iso | en | |
| dc.subject | 控制變異 | zh_TW |
| dc.subject | 亞式選擇權 | zh_TW |
| dc.subject | 重要抽樣法 | zh_TW |
| dc.subject | control variate | en |
| dc.subject | Asian options | en |
| dc.subject | importance sampling | en |
| dc.title | 控制變異法結合重要抽樣法在亞式選擇權定價之應用 | zh_TW |
| dc.title | Combinations of control variate and importance sampling method on pricing Asian options | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 102-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 姜祖恕,吳慶堂 | |
| dc.subject.keyword | 控制變異,亞式選擇權,重要抽樣法, | zh_TW |
| dc.subject.keyword | control variate,importance sampling,Asian options, | en |
| dc.relation.page | 38 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2014-08-20 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-103-1.pdf 未授權公開取用 | 2.06 MB | 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。