請用此 Handle URI 來引用此文件：
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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 呂育道 | |
| dc.contributor.author | Chia-Ting Huang | en |
| dc.contributor.author | 黃佳婷 | zh_TW |
| dc.date.accessioned | 2021-05-20T21:38:40Z | - |
| dc.date.available | 2010-08-16 | |
| dc.date.available | 2021-05-20T21:38:40Z | - |
| dc.date.copyright | 2010-08-16 | |
| dc.date.issued | 2010 | |
| dc.date.submitted | 2010-08-14 | |
| dc.identifier.citation | [1] Yung-Chi Chu. Option Pricing with Stochastic Volatility. MBA thesis, NTU, 2006.
[2] Tian-Shyr Dai and Yuh-Dauh Lyuu. The Bino-Trinomial Tree: A Simple Model for Efficient and Accurate Option Pricing. Journal of Derivatives, Vol. 17 (2010), 7–24. [3] S. Heston. A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options. The Review of Financial Studies, 6, No. 2 (1993), 327–343. [4] J. Hilliard and A. Schwartz. Binomial Option Pricing under Stochastic Volatility and Correlated State Variables. Journal of Derivatives, Fall 1996, 23–39. [5] J. Hull and A. White. The Pricing of Options on Assets with Stochastic Volatility. Journal of Finance, 42, No. 2 (June 1987), 281–300. [6] H. Johnson and D. Shanno. Option Pricing when the Variance is Changing. The Journal of Financial and Quantitative Analysis, 22, No. 2 (June 1987), 143–151. [7] Yuh-Dauh Lyuu. Financial Engineering and Computation. Cambridge University, UK, 2002. [8] Yuh-Dauh Lyuu and Chi-Ning Wu. On Accurate and Provably Efficient GARCH Option Pricing Algorithms. Quantitative Finance, 5, No. 2 (April 2005), 181–198. [9] D. B. Nelson and K. Ramaswamy. Simple Binomial Processes as Diffusion Approximations in Financial Models. Review of Financial Studies, Vol. 3 (1990), 393–430. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/10551 | - |
| dc.description.abstract | Hilliard和Schwartz（1996）提出一個雙變數二元樹模型，其模型可以在隨機波動率下評價選擇權，並允許股價與波動率有相關性。本論文旨在探討 Hilliard和 Schwartz（1996）的雙變數二元樹模型演算法之缺點，以及提供一個部分修正方案。論文針對在 Hilliard和Schwartz（1996）模型中會發生錯誤機率的股價二元樹，改用平均數追蹤法建構的三元樹，而波動率還是維持二元樹，稱此架構為雙變數2/3-元樹模型，最後用此模型去評價選擇權。 | zh_TW |
| dc.description.abstract | The bivariate binomial framework of Hilliard and Schwartz (1996) allows non-zero correlation between the stochastic volatility and the underlying process. It can also be used to value American options. This thesis points out the problems with their bivariate binomial model. It also provides a partial solution to deal with those problems.
When pricing options with the Hilliard-Schwartz model, it is easy to demonstrate that incorrect probabilities will occur in some situations. We use the mean-tracking method to construct trinomial trees instead of binomial trees for one dimension. Nevertheless, the stochastic volatility dimension still adopts the binomial tree as Hilliard and Schwartz (1996). The framework will be called the bivariate bino-trinomial model, and it is used to evaluate options. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-20T21:38:40Z (GMT). No. of bitstreams: 1 ntu-99-R97922073-1.pdf: 851509 bytes, checksum: 3ee02a3355d6063cfbcb7b0abae08a0a (MD5) Previous issue date: 2010 | en |
| dc.description.tableofcontents | 目 錄
口試委員會審定書 ........................................................................................................... i 致 謝 ............................................................................................................................... ii 摘 要 ............................................................................................................................... iii Abstract ............................................................................................................................ iv 圖目錄 ............................................................................................................................. vi 表目錄 ............................................................................................................................ vii 第一章 緒論 .................................................................................................................. 1 1.1研究目的與動機 .................................................................................................... 1 1.2論文架構 ................................................................................................................ 2 第二章 Hilliard和Schwartz（1996）的雙變數二元樹模型 ..................................... 3 2.1隨機波動率模型假設 ............................................................................................ 3 2.2 建構雙變數二元樹 ............................................................................................... 3 2.3 跳動幅度和聯合機率 ........................................................................................... 5 2.4 Hilliard和Schwartz（1996）演算法的問題 ....................................................... 7 第三章 雙變數2/3-元樹模型 ....................................................................................... 9 3.1 隨機波動率模型假設與轉換 ............................................................................... 9 3.2平均數追蹤法（mean-tracking method） ............................................................ 9 3.3 跳動幅度和聯合機率 ......................................................................................... 16 第四章 數值資料與分析 ............................................................................................ 19 第五章 結論與展望 .................................................................................................... 25 附 錄 .............................................................................................................................. 26 參考文獻 ........................................................................................................................ 36 | |
| dc.language.iso | zh-TW | |
| dc.title | 在隨機波動率下之雙變數樹評價模型 | zh_TW |
| dc.title | On Bivariate Lattices for Option Pricing under Stochastic Volatility Models | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 98-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 戴天時,金國興 | |
| dc.subject.keyword | 隨機波動率,雙變數2/3-元樹模型, | zh_TW |
| dc.subject.keyword | stochastic volatility,bivariate bino-trinomial model, | en |
| dc.relation.page | 36 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2010-08-15 | |
| dc.contributor.author-college | 電機資訊學院 | zh_TW |
| dc.contributor.author-dept | 資訊工程學研究所 | zh_TW |
| 顯示於系所單位： | 資訊工程學系 | |
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