利率價差選擇權之評價：Gaussian HJM利率模型

Valuation of Interest Rate Spread Options in a Gaussian Hjm Model

許志成(Chih-Chen Hsu) ； 吳庭斌(Ting-Pin Wu)

《中國統計學報》 50卷1期 (2012/03) Pp. 21-47

https://doi.org/10.29973/JCSA.201203.0002

摘要

本文針對利率價差選擇權（Interest Rate Spread Option）之定價進行研究，其中包含殖利率價差選擇權與LIBOR利率價差選擇權。由於此類利率價差選擇權之封閉解（Close-form Solution）並不存在，本研究利用Borovkova等人（2007）提出的方法，在Heath-Jarrow-Morton（HJM）多因子利率模型下，建構近似利率價差選擇權解析解。推衍所得之近似解析解，在不同期初期間結構與波動度期間結構下，藉由蒙地卡羅模擬（Monte Carlo Simulation）驗證此近似解之準確性，分析結果顯示本研究所推衍之殖利率價差選擇權與LIBOR利率價差選擇權評價模型在不同的利率期間結構下與不同的價值狀況（moneyness）有更準確之評價能力，而且多因子利率模型比單因子利率模型有更準確之評價能力，本研究所推衍出之近似利率價差模型對實務業者在利率價差選擇權評價之應用上提供顯著貢獻。

關鍵字

利率價差選擇權 ； 近似封閉解 ； HJM模型 ； 多因子利率模型

並列摘要

This paper develops two interest rate spread option pricing models: yield cure spread option and LIBOR interest rate spread option. As there is no analytical solution to our investigative topic, this study employs approximation method (Borokova et al, 2007) to develop the closed-form solution to the both spread options models within the high dimensions Gaussian Heath-Jarrow-Morton (HJM) interest rate framework. The numerical investigation is conducted by Monte Carlo simulation that it illustrates the pricing properties of the developed models such as the volatilities of interest rates and the initial term structure of interest rate. The developed models reveal accurate pricing ability within the scenarios of different types of term structures and moneyness. This study contributes significant pricing efforts to practitioner in the interest rate spread option valuation.

並列關鍵字

Interest rate spread option ； closed-form approximation ； HJM model ； multiple factors interest rate model

參考文獻

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