A Continuous Time Model for Interest Rate with Autoregressive and Moving Average Components
A Continuous Time Model for Interest Rate with Autoregressive and Moving Average Components
复制标题
具有自回归和移动平均分量的连续时间利率模型
DOI：
10.1063/1.3498530
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Valeri I. Zakamouline
中科院分区：
文献类型：
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作者：
F. Benth;Steen Koekebakker;Valeri I. Zakamouline
在本文中，我们提出了一个多因素连续时间自回归移动平均（CARMA）模型的短期和远期利率。该模型能够对短期和远期利率动态进行更充分的统计描述。我们证明了这是一个易于处理的期限结构模型，并提供了债券和债券期权价格、债券收益率和远期利率波动率期限结构的封闭解。我们证明了我们的模型的能力，通过校准它的市场数据，并表明它可以重现相当复杂的形状的经验波动率期限结构。特别是，三因子CARMA模型可以轻松捕获期限结构模型中广泛记录的水平、斜率和曲率因子的动态变化。
In this paper we present a multi‐factor continuous‐time autoregressive moving‐average (CARMA) model for the short and forward interest rates. This models is able to present a more adequate statistical description of the short and forward rate dynamics. We show that this is a tractable term structure model and provide closed‐form solutions to bond and bond option prices, bond yields, and the forward rate volatility term structure. We demonstrate the capabilities of our model by calibrating it to market data and show that it can reproduce rather complex shapes of the empirical volatility term structure. In particular, a three‐factor CARMA model can easily capture the dynamics of the level, slope, and curvature factors widely documented in term structure models.