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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 呂育道 | |
| dc.contributor.author | Ming-Hsin Chou | en |
| dc.contributor.author | 周明鑫 | zh_TW |
| dc.date.accessioned | 2021-06-08T00:46:07Z | - |
| dc.date.copyright | 2015-08-07 | |
| dc.date.issued | 2015 | |
| dc.date.submitted | 2015-07-30 | |
| dc.identifier.citation | [1] Bank for International Settlements. “Revisions to the Basel II Market Risk Framework.” Basel Committee on Banking Supervision, Bank for International Settlements, Basel, Switzerland, February 2011.
[2] N.A. Beliaeva and S.K. Nawalka. “A Simple Approach to Pricing American Options Under the Heston Stochastic Volatility Model.” Journal of Derivatives, 17, No. 4 (Summer 2010), 25–43. [3] F. Black and M. Sholes. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81, No. 3 (May–June 1973), 637–654. [4] M. Broadie and O. Kaya. “Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes.” Operations Research, 54 (2006), 217–231 [5] P. Carr and D.B. Madan. “Option Valuation Using the Fast Fourier Transform. ”Journal of Computational Finance, 2, No. 4 (Summer 1999), 61–73 [6] J.H. Chan and M. Joshi. “Fast and Accurate Long-Stepping Simulation of the Heston Stochastic Volatility Model.” Journal of Computational Finance, 16, No. 3 (Spring 2013), 47–97. [7] B. Chen, W.Y. Hsu, J.M. Ho and M.Y. Kao. “Linear-Time Accurate Lattice Algorithms for Tail Conditional Expectation.” Algorithmic Finance, 3, No. 1–2 (2014), 87–140. [8] P. Christoffersen, S.L. Heston, K. Jocobs. “The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well.” Management Science, 55, No. 12 (December 2009), 1914–1932. [9] J.C. Cox, J.E. Ingersoll, S.A. Ross. “A Theory of the Term Structure of Interest Rates.” Econometrica, 53, No. 2 (March 1985), 385–407. [10] J.C. Cox, S.A. Ross, and M. Rubinstein. “Option Pricing: A Simplified Approach.” Journal of Financial Economics, 7, No. 3 (September 1979), 229–263. [11] D. Duffie, and J. Pan. “An Overview of Value at Risk.” Journal of Derivatives, 4, No. 3 (Spring 1997), 7–49. [12] J.H. Guo, and M.W. Hung. “Implementation Problems and Solutions in Stochastic Volatility Models of the Heston Type.” In Handbook of Quantitative Finance and Risk Management, Chapter 75, Springer, New York, US, 2010. [13] S.L. Heston. “A Closed-Form Solution for Options with Stochastic Volatility with Application to Bond and Currency.” Review of Financial Studies, 6, No. 2 (April 1993), 327–343. [14] J. Hull, and A. White. “The Pricing of Options with Stochastic Volatilities.” Journal of Finance, 42, No. 2 (June 1987), 281–300. [15] J. Hull, and A. White. “Valuing Derivative Securities Using the Explicit Finite Dif- ference Method.” Journal of Financial and Quantitative Analysis, 25, No. 1 (March 1990), 87–100. [16] D.P.J. Leisen. “Stock Evolution Under Stochastic Volatility: A Discrete Approach.” Journal of Derivatives, 8, No. 2 (Winter 2000), 9–27. [17] Y.D. Lyuu. Financial Engineering and Computation: Principles, Mathematics, and Algorithms. Cambridge University Press, Cambridge, UK, 2002. [18] N. Moodley. The Heston Model: A Practical Approach with Matlab Code. Programme in Advanced Mathematics of Finance, University of the Witwatersrand, Johannesburg, South Africa, 2005. Retrieved June 21, 2015, from http://math.nyu.edu/~atm262/fall06/compmethods/a1/nimalinmoodley.pdf [19] S.K. Nawalkha, and N. Beliaeva. “Efficient Trees for CIR and CEV Short Rate Models.” Journal of Alternative Investments, 10, No. 1 (Summer 2007), 71–90. [20] D.B. Nelson, and K. Ramaswamy. “Simple Binomial Process as Diffusion Approximations in Financial Models.” Review of Financial Studies, 3, No. 3 (July 1990), 393–430. [21] E. Stein, and J. Stein. “Stock Price Distributions with Stochastic Volatility: An Analytic Approach.” Review of Financial Studies, 4, No. 4 (October 1991), 727–752. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/17916 | - |
| dc.description.abstract | Heston 模型是最廣為人知的隨機波動度模型。然而 Heston 模型的 樹狀評價方法卻相對稀少。本研究使用 Nawalka-Beliaeva 樹狀模型離 散化 Heston 模型中的變異數隨機過程。我們正交化股價隨機過程與變 異數隨機過程後,建立一個五元樹與一個六元樹來評價選擇權的價格。 用我們提出的樹狀模型計算歐式選擇權的價格,並將之與其他數值方 法做比較,結果顯示我們的六元樹可以精確且有效率的算出選擇權的 價格。除此之外,我們用六元樹計算在 Heston 模型下,歐式選擇權的 風險值 (value-at-risk),並與在 Black-Scholes 模型下所得之值做比較。 比較結果發現兩者的風險值有相當程度的差異,此差異可以作為交易 時的一些參考。 | zh_TW |
| dc.description.abstract | Heston’s model ranks among the most popular stochastic-volatility mod- els. However, trees for the Heston model are few. In this thesis, we use the Nawalkha-Beliaeva tree to discretize the variance process of the Heston model. After decorrelating the stock price process and the variance process, a pentanomial and a hexanomial trees are built. Numerical results for European options are presented and analyzed. Comparisons are made with competing numerical methods. Our hexanomial tree is found to be both accurate and ef- ficient. The value-at-risk numbers calculated by our tree for the Heston model are compared with those under the Black-Scholes model. The results show that they are significantly different, which suggests trading opportunities. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T00:46:07Z (GMT). No. of bitstreams: 1 ntu-104-R02723073-1.pdf: 702519 bytes, checksum: ff2c2c501f23a5b4303d0dc00cc676b5 (MD5) Previous issue date: 2015 | en |
| dc.description.tableofcontents | 口試委員會審定書 iii
誌謝 v 摘要 vii Abstract ix 1 Introduction 1 2 The Heston model 5 3 The NB tree for the variance process 7 4 Decorrelation of the stock price process from the variance process 15 5 The underlying grid of our tree 17 6 Successor nodes of our pentanomial tree 21 7 Grid spacing and successor nodes of our hexanomial tree 27 8 Numerical Results 29 9 The Impact of the Heston model on VaR 35 10 Conclusion 39 A Validity of transition probabilities for trinomial tree 41 Bibliography 45 | |
| dc.language.iso | en | |
| dc.title | 隨機波動度 Heston 模型下之效率樹狀模型 | zh_TW |
| dc.title | An Efficient Tree for the Heston Stochastic-Volatility Model | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 103-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 戴天時,金國興,張經略,王釧茹 | |
| dc.subject.keyword | Heston模型,衍生性金融商品,樹狀模型,複雜度,風險值, | zh_TW |
| dc.subject.keyword | Heston model,Derivative,Tree,Complexity,VaR, | en |
| dc.relation.page | 47 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2015-07-31 | |
| 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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