The goal of the paper is twofold. On the one hand, we develop the first term structure framework which takes 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. On the other hand, we provide a general analysis of multiple curve markets under minimal assumptions in an extended HJM framework. In this setting, we characterize absence of arbitrage by means of NAFLVR and provide a fundamental theorem of asset pricing for multiple curve markets. The approach with stochastic discontinuities permits to embed market models directly, thus unifying seemingly different modeling philosophies. We also develop a new tractable class of models, based on affine semimartingales, going beyond the classical requirement of stochastic continuity. Due to the generality of the setting, the existing approaches in the literature can be embedded as special cases.Date: July 24, 2019. 2010 Mathematics Subject Classification. 60G44, 60G57, 91G20, 91G30. JEL classification: C02, C60, E43, G12.

Calibration is a highly challenging task, in particular in multiple yield curve markets. This paper is a first attempt to study the chances and challenges of the application of machine learning techniques for this. We employ Gaussian process regression, a machine learning methodology having many similarities with extended Kálmán filtering, which has been applied many times to interest rate markets and term structure models. We find very good results for the single-curve markets and many challenges for the multi-curve markets in a Vasiček framework. The Gaussian process regression is implemented with the Adam optimizer and the non-linear conjugate gradient method, where the latter performs best. We also point towards future research.

No abstract

No abstract

In this paper, we consider a market with a term structure of credit risky bonds in the single-name case. We aim at minimal assumptions extending existing results in this direction: first, the random field of forward rates is driven by a general semimartingale. Second, the Heath–Jarrow–Morton (HJM) approach is extended with an additional component capturing those future jumps in the term structure which are visible from the current time. Third, the associated recovery scheme is as general as possible, it is only assumed to be nonincreasing. In this general setting, we derive generalized drift conditions which characterize when a given measure is a local martingale measure, thus yielding no asymptotic free lunch with vanishing risk (NAFLVR), the right notion for this large financial market to be free of arbitrage.