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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/58114完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 蔣明晃(Ming-Huang Chiang) | |
| dc.contributor.author | Tzu-Cheng Chuang | en |
| dc.contributor.author | 莊子承 | zh_TW |
| dc.date.accessioned | 2021-06-16T08:06:13Z | - |
| dc.date.available | 2019-07-04 | |
| dc.date.copyright | 2014-07-04 | |
| dc.date.issued | 2014 | |
| dc.date.submitted | 2014-06-21 | |
| dc.identifier.citation | Hansjorg Albrecher, Philipp Mayer, Wim Schoutens, and Jurgen Tistaert, “The Little Heston Trap”, Wilmott Magazine, pp. 83–92, 2007.
Natalia Beliaeva and Nawalkha Sanjay, “A Simple Approach to Pricing American Options under the Heston Stochastic Volatility Model”, The Journal of Derivatives 17 (4), pp. 25–43, 2010. Fischer Black and Myron Scholes, “The Pricing of Options and Corporate Liabilities”. Journal of Political Economy 81 (3), pp. 637–654, 1973. Michael Brennan and Eduardo Schwartz, “Finite Difference Methods and Jump Processes Arising in the Pricing of Contingent Claims: A Synthesis”. Journal of Financial and Quantitative Analysis 13 (3), pp. 461–474, September 1978. Tomas Bjork, “Arbitrage Theory in Continuous Time”, Oxford University Press, 3rd edition, 2009. John Cox, Stephen Ross, and Mark Rubinstein, “Option pricing: A Simplified Approach”, Journal of Financial Economics 7 (3), pp. 229–263, 1979. Jim Gatheral, “The Volatility Surface: A Practitioners’s Guide”, Wiley, 2006. John Cox, Jonathan Ingersoll, and Stephen Ross, “A Theory of the Term Structure of Interest Rates”. Econometrica 53, pp. 385–407, 1985. Lech Grzelak and Kees Oosterlee, “On the Heston Model with Stochastic Interest Rates”, SIAM Journal on Financial Mathematics 2 (1), pp. 255–286, 2009 David Heath, Robert Jarrow, and Andrew Morton, “Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation”. Journal of Financial and Quantitative Analysis, 25, pp.419–440, 1990. Steven Heston, “A Closed–Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options”. The Review of Financial Studies 6 (2), pp. 327–343, 1993. Jim Hilliard and Adam Schwartz, “Binominal Option Pricing Under Stochastic Volatility and Correlated State Variables”, Journal of Derivatives 4 (1), pp. 23–39, 1996. Thomas Ho and Sang Bin Lee, “Term Structure Movements and Pricing Interest Rate Contingent Claims”, Journal of Finance 41, pp. 1011–1029, 1986. John Hull and Alan White, “The Pricing of Options on Assets with Stochastic Volatility”, Journal of Finance 42, pp. 281–300, 1987. John Hull and Alan White, “Valuing Derivative Securities Using the Explicit Finite Difference Method”, Journal of Financial and Quantitative Analysis 25(1), pp. 87–100, 1990. John Hull and Alan White, “Pricing Interest Rate Derivative Securities”, The Review of Financial Studies 3 (4), pp. 573–392, 1990. John Hull and Alan White, “Numerical Procedures for Implementing Term Structure Models I: Single–Factor Models”, Journal of Derivatives 2 (4), pp. 7–16, 1994. John Hull and Alan White, “Using Hull-White Interest Rate Trees”, Journal of Derivatives 3 (3), pp. 26–36, 1996. John Hull, “Options, Futures, and Other Derivatives”, 9th Edition, Prentice Hall, 2008. Francis Longstaff and Eduardo Schwartz, “Valuing American Options by Simulation: A Simple Least-Squares Approach”, The Review of Financial Studies 14, pp. 113–147, 2001. Dietmar Leisen,“Stock Evolution Under Stochastic Volatility: A Discrete Approach,” Journal of Derivatives 8 (2), pp. 9-27, 2000. Daniel Nelson and Krishna Ramaswamy, “Simple Binomial Processes as Diffusion Approximations in Financial Models”, The Review of Financial Studies 3, pp. 393–430, 1990. Saikat Nandi, “How Important Is the Correlation between Returns and Volatility in a Stochastic Volatility Model? Empirical Evidence from Pricing and Hedging in the S&P 500 Index Options Market”, Journal of Banking & Finance 22 (5), pp. 589–610, 1998. Mark Rubinstein, “Implied Binomial Trees”, Journal of Finance 49, 771–818, 1994. Peter Ruckdeschel, Tilman Sayer, and Alexander Szimayer, “Pricing American Options in the Heston Model: A Close Look at Incorporating Correlation”, Journal of Derivatives 20 (3), pp. 9–29, 2013. Oldrich Vasicek, “An Equilibrium Characterisation of the Term Structure”, Journal of Financial Economics 5 (2): 177–188, 1977. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/58114 | - |
| dc.description.abstract | 過往的利率模型大多以固定的volatility來評價利率未來的走勢，然而依照目前世界財經狀況可以合理推估低利率的時代即將結束，未來利率必定調升的情況下，volatility必定有很明顯的波動。在明顯的波動情況下，我們所使用的利率模型並不符合市場狀況，因此使用過往的模型必定會產生顯著的誤差。為了更符合市場，在論文中我利用Heston模型引入了隨機volatility至利率模型當中，藉由Vasicek模型來預估未來的利率，最後使用樹狀圖的方法來預估出可能的利率走勢。 | zh_TW |
| dc.description.abstract | In the past, most of the short rate models were pricing with constant volatility. However, constant volatility does not fit the real situation of our financial condition now because Janet L. Yellen implied that the interest rate will continuous go up soon in the future. When the interest rate goes up, the volatility of interest rate has significant fluctuation. Consequently, the models we used to simulate the interest rate with constant volatility are out-of-date. From the above, stochastic volatility should apply into interest rate model to get more precise interest rate. I, therefore, apply stochastic volatility into vasicek model with tree based method to elaborate my work in the thesis. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T08:06:13Z (GMT). No. of bitstreams: 1 ntu-103-R00943077-1.pdf: 1129601 bytes, checksum: e13ef339ef36d58ef9e62e4f6d763ca3 (MD5) Previous issue date: 2014 | en |
| dc.description.tableofcontents | Acknowledgement i
中文摘要 i Abstract ii Contents 1 List of Figures 3 List of Tables 4 1. Introduction 5 2. Literature Review 6 2.1 Heston Model and Pricing Methods 6 2.2 Short Rate Model 13 I. The Evolution of the Forward Rate Approach 14 II. The Evolution of the Short-Term Interest Rate 15 2.3 Vasicek Model 16 3. Methodology 18 3.1 Setup and Notation 19 3.2 Construct the Model 20 3.2.1 Binomial Variance Tree Approximation 22 3.2.2 Trinomial Stock Price Tree Approximation 27 3.2.3 Combine Stock and Variance Tree, and Match Correlation 29 4. My Model with Stochastic Volatility 37 4.1 Vasicek model with Stochastic Volatility in Heston Model 37 4.1.1 1st-order Taylor Expansion of the Moment 37 4.1.2 Transition Probability of the Interest Rate Process 43 5. Result 53 5.1 Variance Tree 53 5.2 Interest Rate Tree 55 5.3 Combine Interest Rate and Variance Tree, and Match Correlation 57 6. Conclusion 60 Appendix 61 Derive Equations 61 Transition Probability of the Interest Rate Process 64 Reference 67 | |
| dc.language.iso | en | |
| dc.subject | Vasicek model | zh_TW |
| dc.subject | Heston model | zh_TW |
| dc.subject | moment matching | zh_TW |
| dc.subject | correlation | zh_TW |
| dc.subject | tree method | zh_TW |
| dc.title | 具備隨機波動性的 Vasicek (1976)模型的利率樹 | zh_TW |
| dc.title | A Pricing Tree under the Vasicek (1976) Model with Stochastic V olatility | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 102-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.coadvisor | 李賢源(Shyan-Yuan, Lee) | |
| dc.contributor.oralexamcommittee | 呂育道(Yuh-Dauh Lyuu) | |
| dc.subject.keyword | Vasicek model,Heston model,moment matching,correlation,tree method, | zh_TW |
| dc.relation.page | 70 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2014-06-23 | |
| dc.contributor.author-college | 管理學院 | zh_TW |
| dc.contributor.author-dept | 商學研究所 | zh_TW |
| 顯示於系所單位： | 商學研究所 | |
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