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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/88284
Title: | LIBOR 市場模型的高效樹 An Efficient Tree for the LIBOR Market Model |
Authors: | 許熙康 Hsi-Kang Hsu |
Advisor: | 呂育道 Yuh-Dauh Lyuu |
Keyword: | 三元樹,LMM模型,樹狀模型,利率上限,利率下限,界限期權, trinomial tree,LIBOR market model,lattice model,caplet,floorlet,barrier option, |
Publication Year : | 2023 |
Degree: | 碩士 |
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。 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. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/88284 |
DOI: | 10.6342/NTU202300822 |
Fulltext Rights: | 同意授權(限校園內公開) |
Appears in Collections: | 資訊工程學系 |
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ntu-111-2.pdf Restricted Access | 1.36 MB | Adobe PDF | View/Open |
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