Related papers: Compact Finite Difference Scheme with Hermite Inte…
As is well-known, the advantage of the high-order compact difference scheme (H-OCD) is unconditionally stable and convergent with the order $O(\tau^2+h^4)$ under the maximum norm. In this article, a new numerical gradient scheme based on…
In this paper, we propose an iterative splitting method to solve the partial differential equations in option pricing problems. We focus on the Heston stochastic volatility model and the derived two-dimensional partial differential equation…
We develop a model for indifference pricing in derivatives markets where price quotes have bid-ask spreads and finite quantities. The model quantifies the dependence of the prices and hedging portfolios on an investor's beliefs, risk…
In this paper, we introduce two novel methods to solve the American-style option pricing problem and its dual form at the same time using neural networks. Without applying nested Monte Carlo, the first method uses a series of neural…
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…
We introduce a new method to price American options based on Chebyshev interpolation. In each step of a dynamic programming time-stepping we approximate the value function with Chebyshev polynomials. The key advantage of this approach is…
We propose a new high-order alternating direction implicit (ADI) finite difference scheme for the solution of initial-boundary value problems of convection-diffusion type with mixed derivatives and non-constant coefficients, as they arise…
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…
We extend the scheme developed in B. D\"uring, A. Pitkin, "High-order compact finite difference scheme for option pricing in stochastic volatility jump models", 2019, to the so-called stochastic volatility with contemporaneous jumps (SVCJ)…
The method of constructing Hermite trigonometric polynomials, which interpolate the values of a certain periodic function and its derivatives up to (including ) the -th ( ) order in nodes of a uniform grid, is considered. The proposed…
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…
We describe high order accurate and stable fully-discrete finite difference schemes for the initial-boundary value problem associated with the magnetic induction equations. These equations model the evolution of a magnetic field due to a…
In this article, a three-time levels compact scheme is proposed to solve the partial integro-differential equation governing the option prices under jump-diffusion models. In the proposed compact scheme, the second derivative approximation…
In this paper, we discuss the second-order finite element method (FEM) and finite difference method (FDM) for numerically solving elliptic cross-interface problems characterized by vertical and horizontal straight lines, piecewise constant…
This paper deals with the numerical solution of the Heston partial differential equation that plays an important role in financial option pricing, Heston (1993, Rev. Finan. Stud. 6). A feature of this time-dependent, two-dimensional…
Our goal is to analyze the system of Hamilton-Jacobi-Bellman equations arising in derivative securities pricing models. The European style of an option price is constructed as a difference of the certainty equivalents to the value functions…
We approximate the price of the American put for jump diffusions by a sequence of functions, which are computed iteratively. This sequence converges to the price function uniformly and exponentially fast. Each element of the approximating…
Recently, a 4th-order asymptotic preserving multiderivative implicit-explicit (IMEX) scheme was developed (Sch\"utz and Seal 2020, arXiv:2001.08268). This scheme is based on a 4th-order Hermite interpolation in time, and uses an approach…
A general method for accelerating fixed point schemes for problems related to partial differential equations is presented in this article. The speedup is obtained by training a reduced-order model on-the-fly, removing the need to do an…
Theoretical models applied to option pricing should take into account the empirical characteristics of the underlying financial time series. In this paper, we show how to price basket options when assets follow a shifted log-normal process…