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.
Develops a new method for quantizing rough volatility for volatility derivatives pricing.
A new method for pricing options in subdiffusive models derived from finite differences.
Derives a rough SABR formula for short maturities.
In this article, we combine replication pricing with expectation pricing for derivative trades that are partially collateralized by cash. The derivatives are replicated by underlying assets and cash, using repurchasing agreement (repo) and margining, which incur funding costs. We derive a partial differential equation …
Closed-form relations and approximations for SE(3) derivatives for robust numerical simulations.
Derives equations for systems with external forces using variational methods.
New deep learning solver for high-dimensional derivative pricing.
VIND reduces gradient variance for non-Gaussian approximations.
We consider the problem of numerical approximation for forward-backward stochastic differential equations with drivers of quadratic growth (qgFBSDE). To illustrate the significance of qgFBSDE, we discuss a problem of cross hedging of an insurance related financial derivative using correlated assets. For the convergence…
In this paper we propose a generalized numerical scheme for backward stochastic differential equations(BSDEs). The scheme is based on approximation of derivatives via Lagrange interpolation. By changing the distribution of sample points used for interpolation, one can get various numerical schemes with different stabil…
Derives PDEs for pricing RFR derivatives under a new FMM model.
Efficient numerical method for time-fractional Black-Scholes model.
Model for valuing inflation-linked interest rate derivatives.
We focus on mean-variance hedging problem for models whose asset price follows an exponential additive process. Some representations of mean-variance hedging strategies for jump type models have already been suggested, but none is suited to develop numerical methods of the values of strategies for any given time up to …
Neural and numerical methods approximate G2-structures on Calabi-Yau manifolds.
Paper derives a simplified formula for Expected Improvement using log-transformed data.
We develop a new method to solve complex physics equations more accurately and efficiently.
We derive analytic series representations for European option prices in polynomial stochastic volatility models. This includes the Jacobi, Heston, Stein-Stein, and Hull-White models, for which we provide numerical case studies. We find that our polynomial option price series expansion performs as efficiently and accura…
Proposes a method to train neural networks that solve differential equations faster.
The aim of this work is to provide fast and accurate approximation schemes for the Monte-Carlo pricing of derivatives in the Lévy LIBOR model of Eberlein and Özkan (2005). Standard methods can be applied to solve the stochastic differential equations of the successive LIBOR rates but the methods are generally slow. We …
This paper develops a novel numerical method for pricing American options in a two-asset jump-diffusion model.
A new method for efficiently computing derivatives of skew-symmetric matrix exponentials.
Many complex systems generate multifractal time series which are long-range cross-correlated. Numerous methods have been proposed to characterize the multifractal nature of these long-range cross correlations. However, several important issues about these methods are not well understood and most methods consider only o…
Approximates derivative pricing under fractional stochastic volatility.
Using stochastic gradient search and the optimal filter derivative, it is possible to perform recursive (i.e., online) maximum likelihood estimation in a non-linear state-space model. As the optimal filter and its derivative are analytically intractable for such a model, they need to be approximated numerically. In [Po…
Study methods to recover unknown processes in PDEs from data.
We introduce a Vasicek-type short rate model which has two additional parameters representing memory effect. This model presents better results in yield curve fitting than the classical Vasicek model. We derive closed-form expressions for the prices of bonds and bond options. Though the model is non-Markov, there exist…
We discuss two numerical methods, based on a path integral approach described in a previous paper (I), for solving the stochastic equations underlying the financial markets: the Monte Carlo approach, and the Green function deterministic numerical method. Then, we apply the latter to some specific financial problems. In…
In this report, we derive a non-negative series expansion for the Jensen-Shannon divergence (JSD) between two probability distributions. This series expansion is shown to be useful for numerical calculations of the JSD, when the probability distributions are nearly equal, and for which, consequently, small numerical er…
Model accurately calibrates FX market skew for exotic options.
Modeling counterparty risk is computationally challenging because it requires the simultaneous evaluation of all the trades with each counterparty under both market and credit risk. We present a multi-Gaussian process regression approach, which is well suited for OTC derivative portfolio valuation involved in CVA compu…
Paper introduces robust learning methods using coordinate gradient descent.
Study simulates Variance Gamma processes for energy derivatives pricing.
We derive high-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids. The schemes are fourth-order accurate in space and second-order accurate in time for vanishing correlation. In our numerical study we obtain high-order numerical convergence also for non-zero …
In this paper we present qualitative and quantitative comparison of various analytical and numerical approximation methods for calculating a position of the early exercise boundary of the American put option paying zero dividends. First we analyze their asymptotic behavior close to expiration. In the second part of the…
The study analyzes numerical stability in large language models using mixed-precision arithmetic.
We present a numerical implementation of the geodesic ray transform and its inversion over functions and solenoidal vector fields on two-dimensional Riemannian manifolds. For each problem, inversion formulas previously derived in \cite{Pestov2004,Krishnan2010} are implemented in the case of simple and some non-simple m…
The paper calculates XVA for complex basket derivatives using machine learning.
We derive semi-analytic approximation formulae for bond and swaption prices in a Black-Karasiński interest rate model. Approximations are obtained using a novel technique based on the Karhunen-Loève expansion. Formulas are easily computable and prove to be very accurate in numerical tests. This makes them useful for nu…
New formulas derived for variance gamma model option pricing.
The Heston stochastic volatility model is a standard model for valuing financial derivatives, since it can be calibrated using semi-analytical formulas and captures the most basic structure of the market for financial derivatives with simple structure in time-direction. However, extending the model to the case of time-…
Study normal tempered stable processes for energy derivative pricing.
Automatic differentiation is involved for long in applied mathematics as an alternative to finite difference to improve the accuracy of numerical computation of derivatives. Each time a numerical minimization is involved, automatic differentiation can be used. In between formal derivation and standard numerical schemes…
Model prices commodity futures and index options.
Detects arbitrage in multi-asset derivatives markets.
Quantum algorithms improve calculation of parameter sensitivities in financial derivatives.
The paper uses deep learning to efficiently price Bermudan swaptions.
Deep learning improves probabilistic PPDE solution accuracy.