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英文标题：
《Term Structure Modeling under Volatility Uncertainty》
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作者：
Julian H\\\"olzermann
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最新提交年份：
2021
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英文摘要：
In this paper, we study term structure movements in the spirit of Heath, Jarrow, and Morton [Econometrica 60(1), 77-105] under volatility uncertainty. We model the instantaneous forward rate as a diffusion process driven by a G-Brownian motion. The G-Brownian motion represents the uncertainty about the volatility. Within this framework, we derive a sufficient condition for the absence of arbitrage, known as the drift condition. In contrast to the traditional model, the drift condition consists of several equations and several market prices, termed market price of risk and market prices of uncertainty, respectively. The drift condition is still consistent with the classical one if there is no volatility uncertainty. Similar to the traditional model, the risk-neutral dynamics of the forward rate are completely determined by its diffusion term. The drift condition allows to construct arbitrage-free term structure models that are completely robust with respect to the volatility. In particular, we obtain robust versions of classical term structure models.
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中文摘要：
在本文中，我们以Heath、Jarrow和Morton【计量经济学60（1），77-105）】的精神研究了波动不确定性下的期限结构变动。我们将瞬时正向速率建模为G-布朗运动驱动的扩散过程。G-布朗运动表示波动率的不确定性。在此框架内，我们导出了不存在套利的一个充分条件，即漂移条件。与传统模型不同，漂移条件由几个方程和几个市场价格组成，分别称为风险市场价格和不确定性市场价格。如果没有波动不确定性，漂移条件仍然与经典条件一致。与传统模型类似，远期利率的风险中性动态完全由其扩散项决定。漂移条件允许构建对波动率完全鲁棒的无套利期限结构模型。特别是，我们获得了经典期限结构模型的稳健版本。
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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