Related papers: Calculating the Greeks by Cubature formulas

In this work, we present the methods necessary to price an important set of derivatives on a quantum device while offering an advantage over existing classical methods. The methods developed here, in conjunction with ~\cite{GumaroS2026},…

In this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite…

Accurate crude oil price prediction is crucial for financial decision-making. We propose a novel reservoir computing model for forecasting crude oil prices. It outperforms popular deep learning methods in most scenarios, as demonstrated…

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…

An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and…

Cubature formulas and geometrical designs are described in terms of reproducing kernels for Hilbert spaces of functions on the one hand, and Markov operators associated to orthogonal group representations on the other hand. In this way,…

This study derives the expected liquidity cost when performing the delta hedging process of a European option. This cost is represented by an integration formula that includes European option prices and a certain function depending on the…

We present an alternative formula to price European options through cosine series expansions, under models with a known characteristic function such as the Heston stochastic volatility model. It is more robust across strikes and as fast as…

Here we develop an option pricing method based on Legendre series expansion of the density function. The key insight, relying on the close relation of the characteristic function with the series coefficients, allows to recover the density…

We derive new formulas for the price of the European call and put options in the Black-Scholes model, under the form of uniformly convergent series generalizing previously known approximations. We also provide precise boundaries for the…

Hedging methods to mitigate the exposure of variable annuity products to market risks require the calculation of market risk sensitivities (or "Greeks"). The complex, path-dependent nature of these products means these sensitivities…

In the setting of polynomial jump-diffusion dynamics, we provide an explicit formula for computing correlators, namely, cross-moments of the process at different time points along its path. The formula appears as a linear combination of…

This work illustrates how several new pricing formulas for exotic options can be derived within a Levy framework by employing a unique pricing expression. Many existing pricing formulas of the traditional Gaussian model are obtained as a…

We give a proper fractional extension of the classical calculus of variations by considering variational functionals with a Lagrangian depending on a combined Caputo fractional derivative and the classical derivative. Euler-Lagrange…

The COS method is a very efficient way to compute European option prices under L\'evy models or affine stochastic volatility models, based on a Fourier Cosine expansion of the density, involving the characteristic function. This note shows…

Cubature methods, a powerful alternative to Monte Carlo due to Kusuoka~[Adv.~Math.~Econ.~6, 69--83, 2004] and Lyons--Victoir~[Proc.~R.~Soc.\\Lond.~Ser.~A 460, 169--198, 2004], involve the solution to numerous auxiliary ordinary differential…

We introduce a new type of cubature formula for the evaluation of an integral over the disk with respect to a weight function. The method is based on an analysis of the Fourier series of the weight function and a reduction of the bivariate…

High-order derivatives of Green's functions are a key ingredient in Taylor-based fast multipole methods, Barnes-Hut $n$-body algorithms, and quadrature by expansion (QBX). In these settings, derivatives underpin either the formation,…

Expressions for the derivatives with respect to order of modified Bessel functions evaluated at integer orders and certain integral representations of associated Legendre functions with modulus argument greater than unity are used to…

Kristensen and Mele (2011) developed a new approach to obtain closed-form approximations to continuous-time derivatives pricing models. The approach uses a power series expansion of the pricing bias between an intractable model and some…