以二項樹LIBOR 市場模型評價利率衍生性商品

Abstract

本論文將以LIBOR市場模型為基礎，根據不同期間之節點重合遠期利率樹，提出創新方法建造多期間的遠期利率樹之聯合機率分配。由於LIBOR市場模型存在非馬可夫性質，本論文採用Ho、Stapleton和Subrahmanyam(1995)提供節點重合之造二元樹方法，建構遠期利率樹狀結構LIBOR市場模型。本文將此模型結合Hull-White (1994)同時考慮兩因子的三維度樹狀模型，延伸至不同到期日的利率樹，推導出多期遠期利率樹之聯合機率分配。不但能夠求算不同期間生效的遠期利率之條件機率，且能評價各種型式的利率衍生性商品；並與實務上常用LIBOR市場模型的蒙地卡羅模擬法做比較，證明樹狀方法提供更準確且更有效率的結果。

Pricing interest derivatives with the LIBOR market model (LMM) is hard due to the non-Markov nature of LMM. My thesis follows Ho (2008) to build recombined interest trees with HSS (1995) method. The correlation between two forward rates is modeled by the construction method of the two-dimensional tree procedure suggested by Hull and White (1994b). The proposed lattice method is more efficient in comparison with Monte Carlo simulation in pricing the interest rate derivatives, and more accurate in using Monte Carlo as the benchmark.