Related papers: Calibration of Chaotic Models for Interest Rates
The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…
We study the time-evolution of cumulants of velocities and kinetic energies in the stochastic Kac model for velocity exchange of $N$ particles, with the aim of quantifying how fast these degrees of freedom become chaotic in a time scale in…
The ability to construct a realistic simulator of financial exchanges, including reproducing the dynamics of the limit order book, can give insight into many counterfactual scenarios, such as a flash crash, a margin call, or changes in…
As machine learning models are increasingly deployed in high-stakes environments, ensuring both probabilistic reliability and prediction stability has become critical. This paper examines the interplay between classification calibration and…
The applicability of machine learning for predicting chaotic dynamics relies heavily upon the data used in the training stage. Chaotic time series obtained by numerically solving ordinary differential equations embed a complicated noise of…
This paper presents a new model for options pricing. The Black-Scholes-Merton (BSM) model plays an important role in financial options pricing. However, the BSM model assumes that the risk-free interest rate, volatility, and equity premium…
We propose a new diagnostic for quantum chaos. We show that time evolution of complexity for a particular type of target state can provide equivalent information about the classical Lyapunov exponent and scrambling time as out-of-time-order…
This paper uses the assumptions of ergodicity and a microcanonical distribution to compute estimates of the largest Lyapunov exponents in lower-dimensional Hamiltonian systems. That the resulting estimates are in reasonable agreement with…
This paper addresses the Bayesian calibration of dynamic models with parametric and structural uncertainties, in particular where the uncertain parameters are unknown/poorly known spatio-temporally varying subsystem models. Independent…
We present an approach to the simulation of quantum systems driven by classical stochastic processes that is based on the polynomial chaos expansion, a well-known technique in the field of uncertainty quantification. The polynomial chaos…
Chaotic systems, that have a small Lyapunov exponent, do not obey the common random matrix theory predictions within a wide "weak quantum chaos" regime. This leads to a novel prediction for the rate of heating for cold atoms in optical…
This study investigates the application of machine learning techniques, specifically Neural Networks, Random Forests, and CatBoost for option pricing, in comparison to traditional models such as Black-Scholes and Heston Model. Using both…
The transition from arbitrary to chaotic fluctuation properties in quantum systems is studied in a random matrix model. It is assumed that the Hamiltonian can be written as the sum of an arbitrary and a chaos producing part. The Gaussian…
We have found stable chaotic solutions for optomechanical systems coupled with a Two-Level System or qubit. In this system methods have been found which can be used to Tune in and out of Chaos as well as various n-period motions. This…
Calibrating blackbox machine learning models to achieve risk control is crucial to ensure reliable decision-making. A rich line of literature has been studying how to calibrate a model so that its predictions satisfy explicit finite-sample…
In this paper we develop a tractable structural model with analytical default probabilities depending on some dynamics parameters, and we show how to calibrate the model using a chosen number of Credit Default Swap (CDS) market quotes. We…
Quantum chaotic systems are conjectured to display a spectrum whose fine-grained features (gaps and correlations) are well described by Random Matrix Theory (RMT). We propose and develop a complementary version of this conjecture: quantum…
Catastrophe (CAT) bond markets are incomplete and hence carry uncertainty in instrument pricing. As such various pricing approaches have been proposed, but none treat the uncertainty in catastrophe occurrences and interest rates in a…
We consider stochastic volatility models using piecewise constant parameters. We suggest a hybrid optimization algorithm for fitting the models to a volatility surface and provide some numerical results. Finally, we provide an outlook on…
We introduce a framework for calibrating machine learning models so that their predictions satisfy explicit, finite-sample statistical guarantees. Our calibration algorithms work with any underlying model and (unknown) data-generating…