Hull-White 利率模型在美國公債估值中的研究

本文首先對利率期限結構之傳統理論、現代理論以及隨機積分之模擬進行介紹。傳統理論主要包含預期理論、流動性偏好理論和市場分割理論。現代理論則主要包括靜態利率期限結構模型理論和動態利率期限結構模型理論。本文重點介紹後者，其包括均衡模型和無套利模型。其次本文使用現代理論之下的動態模型之Hull-White模型來估計利率期限結構，對於該模型，本文對其進行分析確定出要估計的三個參數：遠期瞬間利率、回歸均數的速度、擴散係數。本文分別採用 Nelson-Siegel 模型與 Vasicek 利率模型估計得出這些參數。再通過蒙特卡羅模擬得出瞬時利率路徑。最后以得出的利率期限結構曲線來對2018年1月2日之美國公債進行估值。主要創新在於對Hull-White模型之解析式進行轉化，並將蒙特卡洛模擬運用進來。實證結果表明Hull-White模型對美國公債預測價格的估計誤差控制在-0.66%左右。且三種不同類別的國債對應的估值誤差有不同的趨勢。

關鍵字

利率期限結構； Hull-White模型；公債；估值

並列摘要

Firstly, this paper introduces the traditional theory of interest rate term structure, modern term structure and the simulation of stochastic integral. Traditional theory mainly includes expectations theory, liquidity preference theory and market segmentation theory. Modern theory mainly includes the static interest rate term structure model and the dynamic interest rate term structure model. This article focuses on the latter, which includes the equilibrium model and the no-arbitrage model. Secondly, this paper uses the Hull-White model to estimate the term structure of interest rate. For this model, this paper analyzes and determines the three parameters to be estimated: the instantaneous forward rate, mean reversion speed, diffusion coefficient. This paper uses the Nelson-Siegel model and the Vasicek interest rate model to estimate these parameters. The instantaneous interest rate path is then obtained priced by the resulting interest rate curve. The main innovation is the transformation of the analytic formula of the Hull-White model and the application of Monte Carlo simulation. The empirical results show that the Hull-White model controls the estimated error of the U.S. treasury bonds forecast price at around -0.66%.