Phenomenology of the Interest Rate Curve
Phenomenology of the Interest Rate Curve
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利率曲线现象学
DOI：
10.1080/135048699334546
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发表时间：
1997
影响因子：
--
通讯作者：
M. Potters
中科院分区：
文献类型：
--
作者：
J. Bouchaud;Nicolas Sagna;R. Cont;Nicole El;M. Potters
本文基于1990-1996年的数据，对美国远期利率曲线进行了现象学描述。我们发现，平均FRC（从即期汇率衡量）的增长作为到期日的平方根，与一个前因子，这是可比的即期汇率波动。这表明，远期利率市场价格包括风险溢价，与现在和到期日之间即期利率的可能变化相当，这可以理解为“风险价值”类型的定价。然而，瞬时FRC偏离简单的平方根定律。扭曲在一年左右最大，反映了市场对即期汇率局部趋势的预期。这种预期的趋势被证明是根据现货本身的过去行为进行校准的。我们发现，这是一致的波动性“驼峰”周围一年的几个作者（我们确认）。最后，解释大部分FRC波动所需的独立组件的数量被发现是小的。我们合理化这表明，FRC的动态演化包含一个稳定的二阶导数（线张力）项，这往往会抑制短尺度的FRC扭曲。原则上，这种形状依赖的期限可能导致套利。然而，由于交易成本的原因，这种套利在实践中无法实现。我们认为，交易成本（或其他市场的“预防措施”）的存在是至关重要的模型建设，更广泛的一类模型成为有资格代表现实。
This paper contains a phenomenological description of the whole U.S. forward rate curve (FRC), based on an data in the period 1990-1996. We find that the average FRC (measured from the spot rate) grows as the square-root of the maturity, with a prefactor which is comparable to the spot rate volatility. This suggests that forward rate market prices include a risk premium, comparable to the probable changes of the spot rate between now and maturity, which can be understood as a `Value-at-Risk' type of pricing. The instantaneous FRC however departs form a simple square-root law. The distortion is maximum around one year, and reflects the market anticipation of a local trend on the spot rate. This anticipated trend is shown to be calibrated on the past behaviour of the spot itself. We show that this is consistent with the volatility `hump' around one year found by several authors (and which we confirm). Finally, the number of independent components needed to interpret most of the FRC fluctuations is found to be small. We rationalize this by showing that the dynamical evolution of the FRC contains a stabilizing second derivative (line tension) term, which tends to suppress short scale distortions of the FRC. This shape dependent term could lead, in principle, to arbitrage. However, this arbitrage cannot be implemented in practice because of transaction costs. We suggest that the presence of transaction costs (or other market `imperfections') is crucial for model building, for a much wider class of models becomes eligible to represent reality.