A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
We propose a new method for the numerical solution of backward stochastic differential equations (BSDEs) which finds its roots in Fourier analysis. The method consists of an Euler time discretization of the BSDE with certain conditional expectations expressed in terms of Fourier transforms and computed using the fast F…
The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff funct…
Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data implicitly assumes periodicity and bandlimitedness of the signal. In this paper, we…
Random Fourier features is a widely used, simple, and effective technique for scaling up kernel methods. The existing theoretical analysis of the approach, however, remains focused on specific learning tasks and typically gives pessimistic bounds which are at odds with the empirical results. We tackle these problems an…
We introduce a novel harmonic analysis for functions defined on the vertices of a strongly connected directed graph of which the random walk operator is the cornerstone. As a first step, we consider the set of eigenvectors of the random walk operator as a non-orthogonal Fourier-type basis for functions over directed gr…
This paper deals with various topics in analysis on hyperbolic spaces. It surveys some recent progress in non-Euclidean Fourier Analysis and proves some new results for the geodesic Radon transform on hyperbolic spaces.
We provide a bound for the error committed when using a Fourier method to price European options when the underlying follows an exponential \levy dynamic. The price of the option is described by a partial integro-differential equation (PIDE). Applying a Fourier transformation to the PIDE yields an ordinary differential…
Many signals on Cartesian product graphs appear in the real world, such as digital images, sensor observation time series, and movie ratings on Netflix. These signals are "multi-dimensional" and have directional characteristics along each factor graph. However, the existing graph Fourier transform does not distinguish …
The stochastic leverage effect, defined as the standardized covariation between the returns and their related volatility, is analyzed in a stochastic volatility model set-up. A novel estimator of the effect is defined using a pre-estimation of the Fourier coefficients of the return and the volatility processes. The con…
Develops Active Fourier Auditor to estimate ML model properties without reconstructing them.
problem Verifying and auditing properties of Machine Learning models in real-world applications.
method A new framework that quantifies ML model properties using Fourier coefficients, without reconstructing the model.
result Active Fourier Auditor (AFA) is more accurate and sample-efficient than baselines for estimating robustness, individual fairness, and group fairness.
We study the volatility functional inference by Fourier transforms. This spectral framework is advantageous in that it harnesses the power of harmonic analysis to handle missing data and asynchronous observations without any artificial time alignment nor data imputation. Under conditions, this spectral approach is cons…
The COS method proposed in Fang and Oosterlee (2008), although highly efficient, may lack robustness for a number of cases. In this paper, we present a Stable pricing of call options based on Fourier cosine series expansion. The Stability of the pricing methods is demonstrated by error analysis, as well as by a series …
In this paper we consider the problem of calculating the quantiles of a risky position, the dynamic of which is described as a continuous time regime-switching jump-diffusion, by using Fourier Transform methods. Furthermore, we study a classical option-based portfolio strategy which minimizes the Value-at-Risk of the h…
Spread options are a fundamental class of derivative contract written on multiple assets, and are widely used in a range of financial markets. There is a long history of approximation methods for computing such products, but as yet there is no preferred approach that is accurate, efficient and flexible enough to apply …
We compare the CPU effort and pricing biases of seven Fourier-based implementations. Our analyses show that truncation and discretization errors significantly increase as we move away from the Black-Scholes-Merton framework. We rank the speed and accuracy of the competing choices, showing which methods require smaller …
We introduce the formalism of generalized Fourier transforms in the context of risk management. We develop a general framework to efficiently compute the most popular risk measures, Value-at-Risk and Expected Shortfall (also known as Conditional Value-at-Risk). The only ingredient required by our approach is the knowle…
New integral theorems improve density function estimations.
problem Improving density function estimations.
method Integrals based on cyclic functions and Riemann sums, Fourier integral theorem, Monte Carlo methods, variational approach, Cauchy residue theorem.
result Optimal cyclic functions minimize square integrals, improving density estimations.