对数正态利率模型的爆炸行为

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摘要翻译：
我们考虑了一个离散时间终端测度利率为对数正态分布的利率模型。这些模型在金融实践中被用作马尔可夫函数模型的参数版本，或作为对数正态Libor市场模型的近似。我们证明了该模型在高挥发和低挥发两种不同的状态下具有不同的定性行为。这两个体系通过一个尖锐的转变而分离，这类似于凝聚态物理中的相变。我们研究了模型在大波动阶段的行为，并讨论了相变对利率衍生品定价的影响。在波动性较大的阶段，某些期望值和凸性调整具有爆炸性行为。对于足够低的挥发度，caplet smile是对数正态的一个很好的近似，而在大挥发度阶段，模型发展出一个非平凡的caplet偏斜。因此，这里讨论的现象对挥发物施加了一个上限，该模型的行为符合预期。
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英文标题：
《Explosive behavior in a log-normal interest rate model》
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作者：
Dan Pirjol
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最新提交年份：
2013
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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英文摘要：
  We consider an interest rate model with log-normally distributed rates in the terminal measure in discrete time. Such models are used in financial practice as parametric versions of the Markov functional model, or as approximations to the log-normal Libor market model. We show that the model has two distinct regimes, at high and low volatilities, with different qualitative behavior. The two regimes are separated by a sharp transition, which is similar to a phase transition in condensed matter physics. We study the behavior of the model in the large volatility phase, and discuss the implications of the phase transition for the pricing of interest rate derivatives. In the large volatility phase, certain expectation values and convexity adjustments have an explosive behavior. For sufficiently low volatilities the caplet smile is log-normal to a very good approximation, while in the large volatility phase the model develops a non-trivial caplet skew. The phenomenon discussed here imposes thus an upper limit on the volatilities for which the model behaves as intended.
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PDF链接：
https://arxiv.org/pdf/1104.0322

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关键词：利率模型 volatilities Quantitative Implications Applications 具有 model phase 物理 调整