离散时间期限结构理论与一致性再校准模型
Discrete Time Term Structure Theory and Consistent Recalibration Models
摘要：
我们开发的理论和离散时间的前向特征过程的应用程序后，一个开创性的论文扬Kallsen和保罗Krühner。特别强调的是放在动态的波动率曲面，可以很容易地制定和实施从选定的离散的角度来看。在数学方面，我们提供了一个算法回答以下问题：描述一个丰富的，仍然听话的一类离散时间随机过程，其边际分布在初始时间，这是免费的套利。从金融数学的角度出发，我们可以构造具有预先描述的（隐含的）波动率曲面和相当一般的波动率曲面动态的模型。在Rene Carmona和Sergey Nadtochiy工作的基础上，我们分析了切线仿射模型的动力学。我们认为，离散方法由于其技术上的简单性，将是重要的期限结构建模。
英文摘要：
We develop theory and applications of forward characteristic processes in discrete time following a seminal paper of Jan Kallsen and Paul Krühner. Particular emphasis is placed on the dynamics of volatility surfaces which can be easily formulated and implemented from the chosen discrete point of view. In mathematical terms we provide an algorithmic answer to the following question: describe a rich, still tractable class of discrete time stochastic processes, whose marginal distributions are given at initial time and which are free of arbitrage. In terms of mathematical finance we can construct models with pre-described (implied) volatility surface and quite general volatility surface dynamics. In terms of the works of Rene Carmona and Sergey Nadtochiy, we analyze the dynamics of tangent affine models. We believe that the discrete approach due to its technical simplicity will be important in term structure modelling.
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