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Term structure modelling for multiple curves with stochastic discontinuities
Finance and Stochastics ( IF 1.7 ) Pub Date : 2020-02-14 , DOI: 10.1007/s00780-020-00416-5
Claudio Fontana , Zorana Grbac , Sandrine Gümbel , Thorsten Schmidt

We develop a general term structure framework taking stochastic discontinuities explicitly into account. Stochastic discontinuities are a key feature in interest rate markets, as for example the jumps of the term structures in correspondence to monetary policy meetings of the ECB show. We provide a general analysis of multiple curve markets under minimal assumptions in an extended HJM framework and provide a fundamental theorem of asset pricing based on NAFLVR. The approach with stochastic discontinuities permits to embed market models directly, unifying seemingly different modelling philosophies. We also develop a tractable class of models, based on affine semimartingales, going beyond the requirement of stochastic continuity.

中文翻译:

具有随机不连续性的多条曲线的项结构建模

我们开发了一个通用术语结构框架,明确考虑了随机不连续性。随机间断是利率市场的一个关键特征,例如,与欧洲央行货币政策会议相对应的期限结构的跳跃。我们在扩展的HJM框架下以最小的假设对多曲线市场进行一般分析,并提供基于NAFLVR的资产定价的基本定理。具有随机不连续性的方法允许直接嵌入市场模型,从而统一看似不同的建模理念。我们还基于仿射半mart,开发了一类易于处理的模型,超越了随机连续性的要求。
更新日期:2020-02-14
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