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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 韓傳祥 | zh_TW |
| dc.contributor.advisor | Chuan-Hsiang Han | en |
| dc.contributor.author | 陳俊憲 | zh_TW |
| dc.contributor.author | Chun-Hsien Chen | en |
| dc.date.accessioned | 2023-10-03T17:31:41Z | - |
| dc.date.available | 2023-11-09 | - |
| dc.date.copyright | 2023-10-03 | - |
| dc.date.issued | 2023 | - |
| dc.date.submitted | 2023-08-14 | - |
| dc.identifier.citation | H. Albrecher, P. Mayer, W. Schoutens, and J. Tistaert. The little heston trap. Wilmott, (1):83–92, 2007.
P. Carr and D. Madan. Option valuation using the fast Fourier transform. Journal of computational finance, 2(4):61–73, 1999. J. C. Cox, J. E. Ingersoll Jr, and S. A. Ross. A theory of the term structure of interest rates. In Theory of valuation, pages 129–164. World Scientific, 2005. Y. Cui, S. del Baño Rollin, and G. Germano. Full and fast calibration of the heston stochastic volatility model. European Journal of Operational Research, 263(2):625–638, 2017. A. Dembo and O. Zeitouni. Large deviations techniques and applications, volume 38. Springer Science & Business Media, 2009. J. Feng, J.-P. Fouque, and R. Kumar. Small-time asymptotics for fast mean-reverting stochastic volatility models. 2012. M. Forde and A. Jacquier. Small-time asymptotics for implied volatility under the heston model. International Journal of Theoretical and Applied Finance, 12(06):861–876, 2009. J.-P. Fouque and C.-H. Han. A martingale control variate method for option pricing with stochastic volatility. ESAIM: Probability and Statistics, 11:40–54, 2007. W. Gander and W. Gautschi. Adaptive quadrature—revisited. BIT Numerical Mathematics, 40:84–101, 2000. J. Gatheral. The volatility surface: a practitioner’s guide. John Wiley & Sons, 2011. M. Geha, A. Jacquier, and Ž. Žurič. Large and moderate deviations for importance sampling in the heston model. Annals of Operations Research, pages 1–46, 2023. J. Gil-Pelaez. Note on the inversion theorem. Biometrika, 38(3-4):481–482, 1951. S. L. Heston. A closed-form solution for options with stochastic volatility with applications to bond and currency options. The review of financial studies, 6(2):327–343,1993. T. R. Hurd and A. Kuznetsov. Explicit formulas for laplace transforms of stochastic integrals. Markov Processes and Related Fields, 14(2):277–290, 2008. C. Kahl and P. Jäckel. Not-so-complex logarithms in the heston model. Wilmott magazine, 19(9):94–103, 2005. K. Kladívko. Maximum likelihood estimation of the cox-ingersoll-ross process: the matlab implementation. Technical Computing Prague, 7(8):1–8, 2007. R. W. Lee et al. Option pricing by transform methods: extensions, unification, and error control. Journal of Computational Finance, 7(3):51–86, 2004. A. L. Lewis. A simple option formula for general jump-diffusion and other exponential lévy processes. Available at SSRN 282110, 2001. R. Lord and C. Kahl. Optimal fourier inversion in semi-analytical option pricing. 2007. P. Malliavin and M. E. Mancino. A fourier transform method for nonparametric estimation of multivariate volatility. 2009. M. E. Mancino, M. C. Recchioni, and S. Sanfelici. Fourier-Malliavin volatility estimation: Theory and practice. Springer, 2017. M. Schmelzle. Option pricing formulae using fourier transform: Theory and application. Preprint, http://pfadintegral. com, 2010. W. Schoutens, E. Simons, and J. Tistaert. A perfect calibration! now what? The best of Wilmott, page 281, 2003. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/90767 | - |
| dc.description.abstract | 本文旨在研究在Heston模型之下的對隱含波動率曲面校準問題。論文主要由兩個部分組成：首先，我們提出一個兩階段校準程序，有效地結合了來自現貨市場和衍生品市場的訊息。其次，我們聚焦於使用重要抽樣法評價短到期的歐式期權價格。此外，我們對重要抽樣的估計式進行了詳盡的變異數分析，並且顯示在Black-Scholes模型之下，估計式在大偏差理論下是漸近最佳的。 | zh_TW |
| dc.description.abstract | This paper addresses the calibration problem of the implied volatility surface within the framework of the Heston model. It comprises two main parts: firstly, we introduce a two-stage calibration procedure that effectively combines information from both the spot market and the derivative market. Secondly, we focus on the valuation of European options with short maturities, employing the importance sampling technique. Furthermore, we conduct a thorough variance analysis of our importance sampling estimator and show that it is asymptotically optimal under the Black-Scholes case by means of Large Deviation Principle. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-10-03T17:31:41Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2023-10-03T17:31:41Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | 致謝 iii
摘要 v Abstract vii Contents ix List of Figures xi List of Tables xiii Chapter 1 Introduction 1 1.1 Introduction and literature survey 1 Chapter 2 The Heston Model 3 2.1 Model and Notations 3 2.1.1 The Volatility Process 4 2.1.2 Heston parameters 5 2.2 Valuation Problem for European Options 7 2.2.1 The Little Heston Trap 8 2.2.2 Integration Scheme 10 2.3 Heston model under risk-neutral measure 11 Chapter 3 Calibration Methodology 13 3.1 Fourier-Malliavin Volatility Estimation 14 3.2 MLE of CIR process 15 3.2.1 OLS for CIR parameter estimation 16 3.2.2 Maximum likelihood estimation 17 3.2.3 Calibration procedure 17 Chapter 4 Importance sampling scheme for short maturity pricing 19 4.1 Motivation 19 4.2 Black-Scholes case 21 4.2.1 Derivation of small time rate function 21 4.2.2 Variance Analysis of the IS estimator 22 4.3 Heston case 25 4.3.1 Small time rate function 26 4.3.2 Variance Analysis of the IS estimator 26 Chapter 5 Numerical Results 31 5.1 Calibration 31 5.2 Importance sampling 35 5.2.1 Range of parameters 37 Chapter 6 Conclusion 41 References 43 | - |
| dc.language.iso | en | - |
| dc.subject | 重要抽樣法 | zh_TW |
| dc.subject | 大離差理論 | zh_TW |
| dc.subject | 模型校準 | zh_TW |
| dc.subject | Heston 模型 | zh_TW |
| dc.subject | 最大概似估計 | zh_TW |
| dc.subject | 隱含波動率 | zh_TW |
| dc.subject | 蒙地卡羅方法 | zh_TW |
| dc.subject | calibration | en |
| dc.subject | Monte Carlo | en |
| dc.subject | implied volatility | en |
| dc.subject | maximum likelihood estimation | en |
| dc.subject | Heston model | en |
| dc.subject | importance sampling | en |
| dc.subject | Large Deviation Principle | en |
| dc.title | Heston隨機波動模型下對短到期隱含波動率曲面之校準 | zh_TW |
| dc.title | Calibration of Short-Dated Implied Volatility Surface under Heston Model | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 111-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 江彌修;孫立憲 | zh_TW |
| dc.contributor.oralexamcommittee | Mi-Hsiu Chiang;Li-Hsien Sun | en |
| dc.subject.keyword | 模型校準,Heston 模型,最大概似估計,隱含波動率,蒙地卡羅方法,重要抽樣法,大離差理論, | zh_TW |
| dc.subject.keyword | calibration,Heston model,maximum likelihood estimation,implied volatility,Monte Carlo,importance sampling,Large Deviation Principle, | en |
| dc.relation.page | 44 | - |
| dc.identifier.doi | 10.6342/NTU202304144 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2023-08-14 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 應用數學科學研究所 | - |
| dc.date.embargo-lift | 2028-08-12 | - |
| 顯示於系所單位： | 應用數學科學研究所 | |
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