Related papers: Efficient exposure computation by risk factor deco…
We introduce a new method to calculate the credit exposure of European and path-dependent options. The proposed method is able to calculate accurate expected exposure and potential future exposure profiles under the risk-neutral and the…
This paper considers the problem of measuring the credit risk in portfolios of loans, bonds, and other instruments subject to possible default under multi-factor models. Due to the amount of the portfolio, the heterogeneous effect of…
Every "x"-adjustment in the so-called xVA financial risk management framework relies on the computation of exposures. Considering thousands of Monte Carlo paths and tens of simulation steps, a financial portfolio needs to be evaluated…
In this article, we propose a new numerical approach to high-dimensional partial differential equations (PDEs) arising in the valuation of exotic derivative securities. The proposed method is extended from Reisinger and Wittum (2007) and…
This paper initiates a series of studies on a COS-tensor framework, as an efficient alternative to MC for large and liquid portfolios characterized by a modest number of dominant risk factors but a large number of trades. The framework is…
We describe a regression-based method, generally referred to as the Least Squares Monte Carlo (LSMC) method, to speed up exposure calculations of a portfolio. We assume that the portfolio contains several exotic derivatives that are priced…
The computational complexity of simultaneous inference methods in high-dimensional linear regression models quickly increases with the number variables. This paper proposes a computationally efficient method based on the Moore-Penrose…
In this paper, we study large losses arising from defaults of a credit portfolio. We assume that the portfolio dependence structure is modelled by the Archimedean copula family as opposed to the widely used Gaussian copula. The resulting…
The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the…
This article focuses on covariance estimation for multi-view data. Popular approaches rely on factor-analytic decompositions that have shared and view-specific latent factors. Posterior computation is conducted via expensive and brittle…
The value-at-risk of a delta-gamma approximated derivatives portfolio can be computed by numerical integration of the characteristic function. However, while the choice of parameters in any numerical integration scheme is paramount, in…
High precision analytical approximation is proposed for variance-covariance based risk allocation in a portfolio of risky assets. A general case of a single-period multi-factor Merton-type model with stochastic recovery is considered. The…
We introduce a new numerical approximation method for functionals of factor credit portfolio models based on the theory of mod-$\phi$ convergence and mod-$\phi$ approximation schemes. The method can be understood as providing correction…
We consider the problem of estimating the probability of a large loss from a financial portfolio, where the future loss is expressed as a conditional expectation. Since the conditional expectation is intractable in most cases, one may…
We propose a quantum Monte Carlo scheme capable of extracting large-scale data of R\'enyi entanglement entropy (EE) with high precision and low technical barrier. Instead of directly computing the ratio of two partition functions within…
The challenge to measure exposures regularly forces financial institutions into a choice between an overwhelming computational burden or oversimplification of risk. To resolve this unsettling dilemma, we systematically investigate replacing…
During recent years the counterparty risk subject has received a growing attention because of the so called Basel Accord. In particular the Basel III Accord asks the banks to fulfill finer conditions concerning counterparty credit exposures…
In this work we detail the application of a fast convolution algorithm computing high dimensional integrals to the context of multiplicative noise stochastic processes. The algorithm provides a numerical solution to the problem of…
We extend a recently developed method to solve semi-linear PDEs to the case of a degenerated diffusion. Being a pure Monte Carlo method it does not suffer from the so called curse of dimensionality and it can be used to solve problems that…
Indirect imaging problems in biomedical optics generally require repeated evaluation of forward models of radiative transport, for which Monte Carlo is accurate yet computationally costly. We develop a novel approach to reduce this…