Related papers: Pricing Bermudan Swaption under Two Factor Hull-Wh…
The Box-Muller transform is a widely used method to generate Gaussian samples from uniform samples. Quantum amplitude encoding methods encode the multi-variate normal distribution in the amplitudes of a quantum state. This work presents the…
We study American swaptions in the linear-rational (LR) term structure model introduced in [5]. The American swaption pricing problem boils down to an optimal stopping problem that is analytically tractable. It reduces to a free-boundary…
Kernel density estimation and kernel regression are powerful but computationally expensive techniques: a direct evaluation of kernel density estimates at $M$ evaluation points given $N$ input sample points requires a quadratic…
We present a fast Gauss transform in one dimension using nearly optimal sum-of-exponentials approximations of the Gaussian kernel. For up to about ten-digit accuracy, the approximations are obtained via best rational approximations of the…
We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above…
We propose a scheme for constructing classical spin Hamiltonians from Hunds coupled spin-fermion models in the limit J_H/t \to \infinity. The strong coupling between fermions and the core spins requires self-consistent calculation of the…
In this paper we present two different variants of method for symmetric matrix inversion, based on modified Gaussian elimination. Both methods avoid computation of square roots and have a reduced machine time's spending. Further, both of…
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…
Recently, an Almost-Exact Simulation (AES) scheme was introduced for the Heston stochastic volatility model and tested for European option pricing. This paper extends this scheme for pricing Bermudan and American options under both Heston…
We present a spectrally accurate method for the rapid evaluation of free-space Stokes potentials, i.e. sums involving a large number of free space Green's functions. We consider sums involving stokeslets, stresslets and rotlets that appear…
We present a multigrid iterative algorithm for solving a system of coupled free boundary problems for pricing American put options with regime-switching. The algorithm is based on our recently developed compact finite difference scheme…
We study the ground state quantum spin fluctuations around the N\'eel ordered state for the one-band ($t,U$) Hubbard model on a site-diluted square lattice. An effective spin Hamiltonian, $H_{\rm s}^{(4)}$, is generated using the canonical…
The pricing of Bermudan options amounts to solving a dynamic programming principle, in which the main difficulty, especially in high dimension, comes from the conditional expectation involved in the computation of the continuation value.…
In this paper, two efficient iterative algorithms based on the simpler GMRES method are proposed for solving shifted linear systems. To make full use of the shifted structure, the proposed algorithms utilizing the deflated restarting…
We develop fast approximation algorithms for the minimum-cost version of the Bounded-Degree MST problem (BD-MST) and its generalization the Crossing Spanning Tree problem (Crossing-ST). We solve the underlying LP to within a $(1+\epsilon)$…
This paper develops a novel analytically tractable Neumann series of Bessel functions representation for pricing (and hedging) European-style double barrier knock-out options, which can be applied to the whole class of one-dimensional…
We propose to study a smooth variant of the $\mu$-hybrid inflation model and a non-minimal Higgs model of inflation with quartic non-minimal coupling between the Higgs field and gravity within the context of a realistic GUT gauge group…
The Cheyette model is a quasi-Gaussian volatility interest rate model widely used to price interest rate derivatives such as European and Bermudan Swaptions for which Monte Carlo simulation has become the industry standard. In low…
A new, very fast, implementation of the exact (Fock) exchange operator for electronic structure calculations within the plane-wave pseudopotential method is described in detail for both molecular and periodic systems, and carefully…
Gaussian graphical models can capture complex dependency structures among variables. For such models, Bayesian inference is attractive as it provides principled ways to incorporate prior information and to quantify uncertainty through the…