相关论文: A mixed Monte Carlo and PDE variance reduction met…

We propose a hybrid Monte Carlo (HMC) technique applicable to high-dimensional multivariate normal distributions that effectively samples along chaotic trajectories. The method is predicated on the freedom of choice of the HMC momentum…

We develop the general integral transforms (GIT) method for pricing barrier options in the time-dependent Heston model (also with a time-dependent barrier) where the option price is represented in a semi-analytical form as a two-dimensional…

Estimation and prediction in high dimensional multivariate factor stochastic volatility models is an important and active research area because such models allow a parsimonious representation of multivariate stochastic volatility. Bayesian…

We study nearly unstable bivariate cumulative heavy-tailed INAR($\infty$) processes and show that, under a one-factor parameterization and a suitable scaling, they converge to the rough Heston model. This yields a discrete-time…

A statistical learning approach for parametric PDEs related to Uncertainty Quantification is derived. The method is based on the minimization of an empirical risk on a selected model class and it is shown to be applicable to a broad range…

The present article revisits the Diffusion Operator Integral (DOI) variance reduction technique originally proposed in Heath and Platen (2002) and extends its theoretical concept to the pricing of American-style options under…

This paper deals with the Monte-Carlo methods for evaluating expectations of functionals of solutions to McKean-Vlasov Stochastic Differential Equations (MV-SDE) with drifts of super-linear growth. We assume that the MV-SDE is approximated…

European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving…

It is shown how to obtain accurate values for American options using Monte Carlo simulation. The main feature of the novel algorithm consists of tracking the boundary between exercise and hold regions via optimization of a certain payoff…

We apply the hybrid Monte Carlo (HMC) algorithm to the financial time sires analysis of the stochastic volatility (SV) model for the first time. The HMC algorithm is used for the Markov chain Monte Carlo (MCMC) update of volatility…

Motivated by a challenging problem in financial trading we are presented with a mixture of regressions with variable selection problem. In this regard, one is faced with data which possess outliers, skewness and, simultaneously, due to the…

Pricing exotic multi-asset path-dependent options requires extensive Monte Carlo simulations. In the recent years the interest to the Quasi-monte Carlo technique has been renewed and several results have been proposed in order to improve…

Classical algorithms in numerical analysis for numerical integration (quadrature/cubature) follow the principle of approximate and integrate: the integrand is approximated by a simple function (e.g. a polynomial), which is then integrated…

In 'A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options', Heston proposes a Stochastic Volatility (SV) model with constant interest rate and derives a semi-explicit valuation formula.…

A parsimonious generalization of the Heston model is proposed where the volatility-of-volatility is assumed to be stochastic. We follow the perturbation technique of Fouque et al (2011, CUP) to derive a first order approximation of the…

The Foreign Exchange (Forex) is a large decentralized market, on which trading analysis and algorithmic trading are popular. Research efforts have been focusing on proof of efficiency of certain technical indicators. We demonstrate,…

Derivatives on the Chicago Board Options Exchange volatility index (VIX) have gained significant popularity over the last decade. The pricing of VIX derivatives involves evaluating the square root of the expected realised variance which…

In this paper, we consider three stochastic-volatility models, each characterized by distinct dynamics of instantaneous volatility: (1) a CIR process for squared volatility (i.e., the classical Heston model); (2) a mean-reverting lognormal…

In many applications, such as plasma edge simulation of a nuclear fusion reactor, a coupled PDE/kinetic description is required, which is usually solved with a coupled finite-volume/Monte-Carlo method. Different procedures have been…

We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. This setting is ubiquitous…