Related papers: A Reduced Basis Method for the Simulation of Ameri…
We propose a reduced basis method to solve time-dependent partial differential equations based on the Laplace transform. Unlike traditional approaches, we start by applying said transform to the evolution problem, yielding a…
In this work, we develop a reduced-basis approach for the efficient computation of parametrized expected values, for a large number of parameter values, using the control variate method to reduce the variance. Two algorithms are proposed to…
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…
We introduce a new approach for the numerical pricing of American options. The main idea is to choose a finite number of suitable excessive functions (randomly) and to find the smallest majorant of the gain function in the span of these…
In this paper a simple, effective adaptation of Alternating Direction Implicit (ADI) time discretization schemes is proposed for the numerical pricing of American-style options under the Heston model via a partial differential…
The basis generation in reduced order modeling usually requires multiple high-fidelity large-scale simulations that could take a huge computational cost. In order to accelerate these numerical simulations, we introduce a FOM/ROM hybrid…
This paper examines a semi-analytical approach for pricing American options in time-inhomogeneous models characterized by negative interest rates (for equity/FX) or negative convenience yields (for commodities/cryptocurrencies). Under such…
In many high-frequency simulation workflows, eigenvalue tracking along a parameter variation is necessary. This can become computationally prohibitive when repeated time-consuming eigenvalue problems must be solved. Therefore, we employ a…
In this paper we propose a semi-analytic approach to pricing American options for time-dependent jump-diffusions models with exponential jumps The idea of the method is to further generalize our approach developed for pricing barrier,…
This work considers a weighted POD-greedy method to estimate statistical outputs parabolic PDE problems with parametrized random data. The key idea of weighted reduced basis methods is to weight the parameter-dependent error estimate…
In this paper, we propose a certified reduced basis (RB) method for quasilinear parabolic problems. The method is based on a space-time variational formulation. We provide a residual-based a-posteriori error bound on a space-time level and…
Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…
Binomial tree methods (BTM) and explicit difference schemes (EDS) for the variational inequality model of American options with time dependent coefficients are studied. When volatility is time dependent, it is not reasonable to assume that…
In this work we propose and analyze a weighted proper orthogonal decomposition method to solve elliptic partial differential equations depending on random input data, for stochastic problems that can be transformed into parametric systems.…
American options are studied in a general discrete market in the presence of proportional transaction costs, modelled as bid-ask spreads. Pricing algorithms and constructions of hedging strategies, stopping times and martingale…
We present a reduced basis method for cheaply constructing (possibly rough) approximations to the nodal basis functions of the virtual element space, and propose to use such approximations for the design of the stabilization term in the…
The offline time of the reduced basis method can be very long given a large training set of parameter samples. This usually happens when the system has more than two independent parameters. On the other hand, if the training set includes…
This paper deals with the numerical approximation of American-style option values governed by partial differential complementarity problems. For a variety of one- and two-asset American options we investigate by ample numerical experiments…
In this paper, we focus on option pricing models based on space-time fractional diffusion. We briefly revise recent results which show that the option price can be represented in the terms of rapidly converging double-series and apply these…
This paper mainly discusses the American option's hedging strategies via binomialmodel and the basic idea of pricing and hedging American option. Although the essential scheme of hedging is almost the same as European option, small…