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.
New approximations for Asian basket spread options using stochastic Taylor expansions.
We consider closed-form approximations for European put option prices within the Heston and GARCH diffusion stochastic volatility models with time-dependent parameters. Our methodology involves writing the put option price as an expectation of a Black-Scholes formula and performing a second-order Taylor expansion aroun…
In this article we develop a method for the strong approximation of stochastic differential equations (SDEs) driven by Lévy processes or general semimartingales. The main ingredients of our method is the perturbation of the SDE and the Taylor expansion of the resulting parameterized curve. We apply this method to devel…
Using classical Taylor series techniques, we develop a unified approach to pricing and implied volatility for European-style options in a general local-stochastic volatility setting. Our price approximations require only a normal CDF and our implied volatility approximations are fully explicit (ie, they require no spec…
In this paper we study the pricing of exchange options when underlying assets have stochastic volatility and stochastic correlation. An approximation using a closed-form approximation based on a Taylor expansion of the conditional price is proposed. Numerical results are illustrated for exchanges between WTI and Brent …
Approximates option prices in Barndorff-Nielsen and Shephard models using Taylor expansion.
Proposes a method for approximating transition densities of SDEs driven by gamma processes.
The paper is concerned with non-linear Gaussian filtering and smoothing in continuous-discrete state-space models, where the dynamic model is formulated as an Itô stochastic differential equation (SDE), and the measurements are obtained at discrete time instants. We propose novel Taylor moment expansion (TME) Gaussian …
We derive asymptotic expansions for the prices of a variety of European and barrier-style claims in a general local-stochastic volatility setting. Our method combines Taylor series expansions of the diffusion coefficients with an expansion in the correlation parameter between the underlying asset and volatility process…
We apply results of Malliavin-Thalmaier-Watanabe for strong and weak Taylor expansions of solutions of perturbed stochastic differential equations (SDEs). In particular, we work out weight expressions for the Taylor coefficients of the expansion. The results are applied to LIBOR market models in order to deal with the …
We propose \emph{Taylorized training} as an initiative towards better understanding neural network training at finite width. Taylorized training involves training the -th order Taylor expansion of the neural network at initialization, and is a principled extension of linearized training---a recently proposed theory …
New formulas for pricing Asian and basket options using stochastic expansion.
Random Function Descent improves optimization in high dimensions.
Modern convolutional networks, incorporating rectifiers and max-pooling, are neither smooth nor convex; standard guarantees therefore do not apply. Nevertheless, methods from convex optimization such as gradient descent and Adam are widely used as building blocks for deep learning algorithms. This paper provides the fi…
Paper presents a new backward deep BSDE method for solving nonlinear FBSDE problems.
Estimates neural drift for stochastic equations, improving inference on noisy data.
We study the finite horizon Merton portfolio optimization problem in a general local-stochastic volatility setting. Using model coefficient expansion techniques, we derive approximations for the both the value function and the optimal investment strategy. We also analyze the `implied Sharpe ratio' and derive a series a…
Paper introduces cubature method for stochastic Volterra equations.
Improved Frank-Wolfe method reduces dependence on data size for empirical risk minimization.
New sampling scheme improves ML accuracy in physics simulations.
New learning algorithm for real analytic functions without gradient descent.
In this paper we propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model, based on Taylor expansions and the calculation of mixed exponential-power moments of a Gaussian distribution. Our numerical results show that a second order expansion provides accurate prices o…
Paper approximates XVA for European contingent claims using BSDEs and polynomial expansions.
This technical report constructs a theoretical framework to relate standard Taylor approximation based optimisation methods with Natural Gradient (NG), a method which is Fisher efficient with probabilistic models. Such a framework will be shown to also provide mathematical justification to combine higher order methods …
Proposes a Taylor framework to unify and analyze attribution methods.
SOAR improves deep networks' robustness against adversarial examples.
In this paper we study the pricing of exchange options under a dynamic described by stochastic correlation with random jumps. In particular, we consider a Ornstein-Uhlenbeck covariance model with Levy Background Noise Process driven by Inverse Gaussian subordinators. We use expansion in terms of Taylor polynomials and …
The paper modifies asset pricing models using Taylor series expansions and market-based averages.
Manifold calculus of functors, due to M. Weiss, studies contravariant functors from the poset of open subsets of a smooth manifold to topological spaces. We introduce "multivariable" manifold calculus of functors which is a generalization of this theory to functors whose domain is a product of categories of open sets. …
This paper provides intuition on the relationship of accrual and mark-to-market valuation for cash and forward interest rate trades. Discounted cashflow valuation is compared to spread-based valuation for forward trades, which explains the trader's view on valuation. This is followed by Taylor series approximation for …
Unified framework for analyzing machine learning model attributions.
New samplers reduce NFEs for diffusion models.
Paper improves kernel approximations for better statistical learning.
In the present paper, a decomposition formula for the call price due to Alòs is transformed into a Taylor type formula containing an infinite series with stochastic terms. The new decomposition may be considered as an alternative to the decomposition of the call price found in a recent paper of Alòs, Gatheral and Radoi…
Proposes a method to estimate SDE noise from a single trajectory.
Paper proposes a closed-form formula for geometric Istanbul call options.
Agents learn state ambiguity from non-linear sensor data using Gaussian approximations.
FBSJNN solves PIDEs and FBSDEJs with deep learning, offering theoretical and numerical efficiency.
Paper proves existence of a CMC hypertorus in 4D sphere using numerical methods.
The paper calculates Bachelier option prices using Taylor expansions and applies it as a variance reduction technique.
This paper optimizes matrix-based Renyi's entropy computation for large datasets.
Kernelized Taylor diagram visualizes data populations with fewer assumptions.
Paper proves existence of solutions for complex surface diffusion equation.
Expanding the rough Heston model in
In this paper, we propose a novel approach to automatically determine the batch size in stochastic gradient descent methods. The choice of the batch size induces a trade-off between the accuracy of the gradient estimate and the cost in terms of samples of each update. We propose to determine the batch size by optimizin…
This paper extends AD techniques to Monte Carlo processes for efficient derivative calculation.
We study differential forms and their higher-order generalizations by interpreting them as functions on map spaces. We get a series of approximations of "generalized manifolds" (i.e. of sheaves and stacks) somewhat akin to Taylor series.
Scannell and Sinha considered a spectral sequence to calculate the rational homotopy groups of spaces of long knots in n-dimensional Euclidean space, for n greater than or equal to 4. At the end of their paper they conjecture that when n is odd, the terms on the antidiagonal on the second page precisely give the space …