LIBOR 市場模型的高效樹

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.