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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/88284完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 呂育道 | zh_TW |
| dc.contributor.advisor | Yuh-Dauh Lyuu | en |
| dc.contributor.author | 許熙康 | zh_TW |
| dc.contributor.author | Hsi-Kang Hsu | en |
| dc.date.accessioned | 2023-08-09T16:21:51Z | - |
| dc.date.available | 2023-11-09 | - |
| dc.date.copyright | 2023-08-09 | - |
| dc.date.issued | 2023 | - |
| dc.date.submitted | 2023-07-18 | - |
| dc.identifier.citation | Black, F. (1976, January). The pricing of commodity contracts. Journal of Financial Economics, 3(1–2), 167–179.
Brace, A., G ̧atarek, D., & Musiela, M. (1997). The market model of interest rate dynamics. Mathematical Finance, 7(2), 127–155. Dai, T.-S., Chung, H.-M., & Ho, C.-J. (2009, Dec). Using the libor market model to price the interest rate derivatives: A recombining binomial tree methodology. NTU Management Review, 20(1), 41–68. Financial Stability Board. (2019). Overnight risk-free rates. a user’s guide. Financial Stability Board. Gyntelberg, J., & Wooldridge, P. (2008). Interbank rate fixings during the recent turmoil. BIS Quarterly Review. Harrison, J., & Kreps, D. M. (1979, June). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20(3), 381–408. Ho, T.-S., Stapleton, R. C., & Subrahmanyam, M. G. (1995, October). Multivariate binomial approximations for asset prices with nonstationary variance and covariance characteristics. Review of Financial Studies, 8(4), 1125–1152. ISDA. (2020). ISDA launches risk-free rate adoption indicator (Tech. Rep.). International Swaps and Derivatives Association. ISDA. (2023a). Progress on global transition to RFRs in derivatives markets (Tech. Rep.). International Swaps and Derivatives Association. ISDA. (2023b). Transition to RFRs review: Full year 2022 and the fourth quarter of 2022 (Tech. Rep.). International Swaps and Derivatives Association. Jäckel, P. (2002). Monte carlo methods in finance. Chichester, West Sussex, U.K.: Wiley. Leisen, D. P. (1998, July). Pricing the American put option: A detailed convergence analysis for binomial models. Journal of Economic Dynamics and Control, 22(8-9), 1419–1444. Lok, U. H., & Lyuu, Y.-D. (2019, December). Efficient trinomial trees for local-volatility models in pricing double-barrier options. Journal of Futures Markets, 40(4), 556–574. Lyashenko, A., & Mercurio, F. (2019). Looking forward to backward-looking rates: A modeling framework for term rates replacing LIBOR. SSRN Electronic Journal. Pelsser, A. (2000). Efficient methods for valuing interest rate derivatives. London: Springer. Tang, Y., & Lange, J. (2001). A nonexploding bushy tree technique and its application to the multifactor interest rate market model. Journal of Computational Finance, 4(4), 5–31. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/88284 | - |
| dc.description.abstract | LIBOR 市場模型(LMM)是一種廣泛用於定價利率衍生品的利率模型。然 而，定價衍生品需要將所有利率帶到同一機率度量下進行。這種轉換使利率不再 呈對數正態分佈並引入了複雜的狀態相依漂移，因此為 LMM 建構一個高效樹模 型變得非常具有挑戰性。本論文提出了用於單因子、常數波動率 LMM 的高效率樹狀模型。我們的演算法為每個 LIBOR 利率構建了一個節點重合的三元樹。此三 元樹可準確的計算出利率上限、利率下限和界限期權的價格。 | zh_TW |
| dc.description.abstract | The LIBOR Market Model (LMM) is a widely used interest rate model for pricing interest rate derivatives. However, pricing derivatives requires bringing all forward rates under the same measure. This introduces a complex state-dependent drift. Consequently, constructing an efficient tree for the LMM becomes challenging. This thesis presents an efficient tree for the single-factor, constant-volatility LMM. Our algorithm constructs a re-combining trinomial tree for each forward LIBOR rate. The proposed tree yields accurate prices for caplets, floorlets and barrier options. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-08-09T16:21:51Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2023-08-09T16:21:51Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | Acknowledgements i
摘要 iii Abstract v Contents vii List of Figures ix List of Tables xi Chapter 1 Introduction 1 Chapter 2 Preliminaries 5 2.1 The LIBOR Market Model (LMM) 5 2.1.1 The LIBOR Rate Process 6 2.1.2 Terminal Measure 6 2.2 Interest Rate Derivatives 7 2.2.1 Caplets and Floorlets 7 2.2.2 Caps and Floors 8 2.2.3 Discrete Barrier Caps/Floors 8 Chapter 3 An Efficient Trinomial Tree for the LMM 11 3.1 Basic Terms 11 3.2 Constructing the ln L_n Tree 12 3.3 Constructing the ln L_i Tree 14 Chapter 4 Numerical Results 19 4.1 Numerical Analysis of the Convergence in Mean and Variance 19 4.2 Valuation of Caplets/Floorlets in the LMM 27 4.3 Valuation of Discrete Barrier Options in the LMM 33 Chapter 5 Conclusion 35 References 37 | - |
| dc.language.iso | en | - |
| dc.subject | 三元樹 | zh_TW |
| dc.subject | LMM模型 | zh_TW |
| dc.subject | 利率上限 | zh_TW |
| dc.subject | 樹狀模型 | zh_TW |
| dc.subject | 利率下限 | zh_TW |
| dc.subject | 界限期權 | zh_TW |
| dc.subject | barrier option | en |
| dc.subject | lattice model | en |
| dc.subject | caplet | en |
| dc.subject | trinomial tree | en |
| dc.subject | floorlet | en |
| dc.subject | LIBOR market model | en |
| dc.title | LIBOR 市場模型的高效樹 | zh_TW |
| dc.title | An Efficient Tree for the LIBOR Market Model | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 111-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 陸裕豪;王釧茹;金國興 | zh_TW |
| dc.contributor.oralexamcommittee | U-Hou Lok;Chuan-Ju Wang;Gow-Hsing King | en |
| dc.subject.keyword | 三元樹,LMM模型,樹狀模型,利率上限,利率下限,界限期權, | zh_TW |
| dc.subject.keyword | trinomial tree,LIBOR market model,lattice model,caplet,floorlet,barrier option, | en |
| dc.relation.page | 38 | - |
| dc.identifier.doi | 10.6342/NTU202300822 | - |
| dc.rights.note | 同意授權(限校園內公開) | - |
| dc.date.accepted | 2023-07-18 | - |
| dc.contributor.author-college | 電機資訊學院 | - |
| dc.contributor.author-dept | 資訊工程學系 | - |
| dc.date.embargo-lift | 2028-07-15 | - |
| 顯示於系所單位： | 資訊工程學系 | |
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