78 citations · 171 across the 33 of their papers we have counts for
44 papers
Moments of polynomial processes under affine resetting
Johannes Assefa, Martin Keller-Ressel, Zbigniew Palmowski
We consider polynomial processes, i.e., continuous-time Markov processes that preserve polynomials without increasing degree, and augment them with resetting. Resetting means that…
Discovering parametrizations of implied volatility with symbolic regression
Martin Keller-Ressel, Hannes Nikulski
We investigate the data-driven discovery of parametric representations for implied volatility slices. Using symbolic regression, we search for simple analytic formulas that approxi…
Moments of generalized fractional polynomial processes
Johannes Assefa, Martin Keller-Ressel
We derive a moment formula for generalized fractional polynomial processes, i.e., for polynomial-preserving Markov processes time-changed by an inverse Lévy-subordinator. If the ti…
Term structure shapes and their consistent dynamics in the Svensson family
Martin Keller-Ressel, Felix Sachse
We examine the shapes attainable by the forward- and yield-curve in the widely-used Svensson family, including the Nelson-Siegel and Bliss subfamilies. We provide a complete classi…
Emergence of heavy tails in homogenized stochastic gradient descent
Zhe Jiao, Martin Keller-Ressel
It has repeatedly been observed that loss minimization by stochastic gradient descent (SGD) leads to heavy-tailed distributions of neural network parameters. Here, we analyze a con…
Hyperbolic Deep Learning in Computer Vision: A Survey
Pascal Mettes, Mina Ghadimi Atigh, Martin Keller-Ressel +2
Deep representation learning is a ubiquitous part of modern computer vision. While Euclidean space has been the de facto standard manifold for learning visual representations, hype…
State space decomposition and classification of term structure shapes in the two-factor Vasicek model
Martin Keller-Ressel, Felix Sachse
Using the concept of envelopes we show how to divide the state space $\RR^2$ of the two-factor Vasicek model into regions of identical term-structure shape. We develop a formula fo…
W-shaped implied volatility curves in a variance-gamma mixture model
Martin Keller-Ressel
In liquid option markets, W-shaped implied volatility curves have occasionally be observed. We show that such shapes can be reproduced in a mixture of two variance-gamma models. Th…
Bartlett's Delta revisited: Variance-optimal hedging in the lognormal SABR and in the rough Bergomi model
Martin Keller-Ressel
We derive analytic expressions for the variance-optimal hedging strategy and its mean-square hedging error in the lognormal SABR and in the rough Bergomi model. In the SABR model,…
Strain-Minimizing Hyperbolic Network Embeddings with Landmarks
Martin Keller-Ressel, Stephanie Nargang
We introduce L-hydra (landmarked hyperbolic distance recovery and approximation), a method for embedding network- or distance-based data into hyperbolic space, which requires only…
Hyperbolic Busemann Learning with Ideal Prototypes
Mina Ghadimi Atigh, Martin Keller-Ressel, Pascal Mettes
Hyperbolic space has become a popular choice of manifold for representation learning of various datatypes from tree-like structures and text to graphs. Building on the success of d…
A Theory of Hyperbolic Prototype Learning
Martin Keller-Ressel
We introduce Hyperbolic Prototype Learning, a type of supervised learning, where class labels are represented by ideal points (points at infinity) in hyperbolic space. Learning is…
The hyperbolic geometry of financial networks
Martin Keller-Ressel, Stephanie Nargang
Based on data from the European banking stress tests of 2014, 2016 and the transparency exercise of 2018 we demonstrate for the first time that the latent geometry of financial net…
The classification of term structure shapes in the two-factor Vasicek model -- a total positivity approach
Martin Keller-Ressel
We provide a full classification of all attainable term structure shapes in the two-factor Vasicek model of interest rates. In particular, we show that the shapes normal, inverse,…
A comparison principle between rough and non-rough Heston models - with applications to the volatility surface
Martin Keller-Ressel, Assad Majid
We present a number of related comparison results, which allow to compare moment explosion times, moment generating functions and critical moments between rough and non-rough Hesto…
Hydra: A method for strain-minimizing hyperbolic embedding of network- and distance-based data
Martin Keller-Ressel, Stephanie Nargang
We introduce hydra (hyperbolic distance recovery and approximation), a new method for embedding network- or distance-based data into hyperbolic space. We show mathematically that h…
Affine Rough Models
Martin Keller-Ressel, Martin Larsson, Sergio Pulido
The goal of this survey article is to explain and elucidate the affine structure of recent models appearing in the rough volatility literature, and show how it leads to exponential…
Affine processes beyond stochastic continuity
Martin Keller-Ressel, Thorsten Schmidt, Robert Wardenga
In this paper we study time-inhomogeneous affine processes beyond the common assumption of stochastic continuity. In this setting times of jumps can be both inaccessible and predic…
Forward-Invariance and Wong-Zakai Approximation for Stochastic Moving Boundary Problems
Martin Keller-Ressel, Marvin S. Mueller
We discuss a class of stochastic second-order PDEs in one space-dimension with an inner boundary moving according to a possibly non-linear, Stefan-type condition. We show that prop…
Affine forward variance models
Jim Gatheral, Martin Keller-Ressel
We introduce the class of affine forward variance (AFV) models of which both the conventional Heston model and the rough Heston model are special cases. We show that AFV models can…
Detecting independence of random vectors: generalized distance covariance and Gaussian covariance
Björn Böttcher, Martin Keller-Ressel, René L. Schilling
Distance covariance is a quantity to measure the dependence of two random vectors. We show that the original concept introduced and developed by Székely, Rizzo and Bakirov can be e…
Distance multivariance: New dependence measures for random vectors
Björn Böttcher, Martin Keller-Ressel, René L. Schilling
We introduce two new measures for the dependence of random variables: distance multivariance and total distance multivariance. Both measures are based on the weighted $L^…
Erratum to: `Yield curve shapes and the asymptotic short rate distribution in affine one-factor models'
Martin Keller-Ressel
This paper corrects an error in [Keller-Ressel, M. and Steiner T. "Yield curve shapes and the asymptotic short rate distribution in affine one-factor models." Finance and Stochasti…
Semi-Static Variance-Optimal Hedging in Stochastic Volatility Models with Fourier Representation
Paolo Di Tella, Martin Haubold, Martin Keller-Ressel
In a financial market model, we consider the variance-optimal semi-static hedging of a given contingent claim, a generalization of the classic variance-optimal hedging. To obtain a…