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Let $X$ be an $N$-dimensional random vector which describes the ordered eigenvalues of a $\beta$-Hermite ensemble, and let $z$ the vector containing the ordered zeros of the Hermite poynomial $H_N$. We present an explicit estimate for…

Probability · Mathematics 2025-02-11 Michael Voit

In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a…

Physics and Society · Physics 2008-12-10 Luca Capriotti

This paper is concerned with the asymptotics for Greeks of European-style options and the risk-neutral density function calculated under the constant elasticity of variance model. Formulae obtained help financial engineers to construct a…

Pricing of Securities · Quantitative Finance 2017-07-17 Oleg L. Kritski , Vladimir F. Zalmezh

The random matrix theory method of planar Gaussian diagrammatic expansion is applied to find the mean spectral density of the Hermitian equal-time and non-Hermitian time-lagged cross-covariance estimators, firstly in the form of master…

Statistical Finance · Quantitative Finance 2012-05-22 Andrzej Jarosz

Given a nonsingular $n \times n$ matrix of univariate polynomials over a field $\mathbb{K}$, we give fast and deterministic algorithms to compute its determinant and its Hermite normal form. Our algorithms use…

Symbolic Computation · Computer Science 2017-03-31 George Labahn , Vincent Neiger , Wei Zhou

We study the distribution of the extended binomial coefficients by deriving a complete asymptotic expansion with uniform error terms. We obtain the expansion from a local central limit theorem and we state all coefficients explicitly as…

Combinatorics · Mathematics 2014-07-29 Thorsten Neuschel

We investigate the limiting distribution of geometric Brownian motion conditional on its running maximum taking large values. We show that the conditional distribution of the geometric Brownian motion converges after a suitable…

Probability · Mathematics 2025-05-14 Ze-An Ng

Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by…

Data Structures and Algorithms · Computer Science 2017-05-16 Aubrey Alston

We present a novel approach for parameter calibration of the Heston model for pricing an Asian put option, namely space mapping. Since few parameters of the Heston model can be directly extracted from real market data, calibration to real…

Numerical Analysis · Mathematics 2025-01-27 Anna Clevenhaus , Claudia Totzeck , Matthias Ehrhardt

Mixture models have found uses in many areas. To list a few: unsupervised learning, empirical Bayes, latent class and trait models. The current applications of mixture models to empirical data is limited to computing a mixture model from…

Computation · Statistics 2015-09-23 Andrew Clark

A fast and accurate algorithm for the computation of Gauss-Hermite and generalized Gauss-Hermite quadrature nodes and weights is presented. The algorithm is based on Newton's method with carefully selected initial guesses for the nodes and…

Numerical Analysis · Mathematics 2014-10-21 Alex Townsend , Thomas Trogdon , Sheehan Olver

We study the short maturity asymptotics for prices of forward start Asian options under the assumption that the underlying asset follows a local volatility model. We obtain asymptotics for the cases of out-of-the-money, in-the-money, and…

Pricing of Securities · Quantitative Finance 2019-08-19 Dan Pirjol , Jing Wang , Lingjiong Zhu

This paper presents a multinomial method for option pricing when the underlying asset follows an exponential Variance Gamma process. The continuous time Variance Gamma process is approximated by a discrete time Markov chain with the same…

Pricing of Securities · Quantitative Finance 2021-06-18 Nicola Cantarutti , João Guerra

For use in calculating higher-order coherent- and squeezed- state quantities, we derive generalized generating functions for the Hermite polynomials. They are given by $\sum_{n=0}^{\infty}z^{jn+k}H_{jn+k}(x)/(jn+k)!$, for arbitrary integers…

Quantum Physics · Physics 2009-10-28 Michael Martin Nieto , D. Rodney Truax

A computational technique borrowed from the physical sciences is introduced to obtain accurate closed-form approximations for the transition probability of arbitrary diffusion processes. Within the path integral framework the same technique…

Physics and Society · Physics 2008-12-10 Luca Capriotti

We study the problem of super-replication for game options under proportional transaction costs. We consider a multidimensional continuous time model, in which the discounted stock price process satisfies the conditional full support…

Portfolio Management · Quantitative Finance 2012-03-12 Yan Dolinsky

We consider a generalization of the classical Hermite polynomials by the addition of terms involving derivatives in the inner product. This type of generalization has been studied in the literature from the point of view of the algebraic…

Classical Analysis and ODEs · Mathematics 2009-09-04 M. Alfaro , J. J. Moreno-Balcazar , A. Pena , M. L. Rezola

We compute Hermite expansions of some tempered distributions by using the Bargmann transform. In other words, we calculate the Taylor expansions of the corresponding entire functions. Our method of computations seems to be superior to the…

Classical Analysis and ODEs · Mathematics 2017-05-03 Hiroyuki Chihara , Takashi Furuya , Takumi Koshikawa

We describe and analyze a numerical algorithm for computing the homology (Betti numbers and torsion coefficients) of real projective varieties. Here numerical means that the algorithm is numerically stable (in a sense to be made precise).…

Algebraic Geometry · Mathematics 2017-05-16 Felipe Cucker , Teresa Krick , Michael Shub

Given a finite set of European call option prices on a single underlying, we want to know when there is a market model which is consistent with these prices. In contrast to previous studies, we allow models where the underlying trades at a…

Mathematical Finance · Quantitative Finance 2019-07-17 Stefan Gerhold , I. Cetin Gülüm