Related papers: Explicit RKF-Compact Scheme for Pricing Regime Swi…
We propose an adaptive and explicit fourth-order Runge-Kutta-Fehlberg method coupled with a fourth-order compact scheme to solve the American put options problem. First, the free boundary problem is converted into a system of partial…
We consider a system of coupled free boundary problems for pricing American put options with regime-switching. To solve this system, we first employ the logarithmic transformation to map the free boundary for each regime to multi-fixed…
When solving the American options with or without dividends, numerical methods often obtain lower convergence rates if further treatment is not implemented even using high-order schemes. In this article, we present a fast and explicit…
We propose a stable sixth-order compact finite difference scheme with a dynamic fifth-order staggered boundary scheme and 3(2) R-K Bogacki and Shampine adaptive time stepping for pricing American style options. To locate, fix and compute…
This paper presents the Runge-Kutta-Legendre finite difference scheme, allowing for an additional shift in its polynomial representation. A short presentation of the stability region, comparatively to the Runge-Kutta-Chebyshev scheme…
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…
In this article, a compact finite difference method is proposed for pricing European and American options under jump-diffusion models. Partial integro-differential equation and linear complementary problem governing European and American…
We study the barrier that gives the optimal time to exercise an American option written on a time-dependent Ornstein--Uhlenbeck process, a diffusion often adopted by practitioners to model commodity prices and interest rates. By framing the…
Explicit Runge-Kutta (RK) integration of hyperbolic initial-boundary value problems with time-dependent Dirichlet data often displays order reduction: the observed convergence order falls below the nominal order because the stage structure…
In this paper, an integral equation representation for the early exercise boundary of an American option contract is considered. Thus far, a number of different techniques have been proposed in the literature to obtain a variety of integral…
In this research work, we propose a high-order time adapted scheme for pricing a coupled system of fixed-free boundary constant elasticity of variance (CEV) model on both equidistant and locally refined space-grid. The performance of our…
The purpose of this survey chapter is to present a transformation technique that can be used in analysis and numerical computation of the early exercise boundary for an American style of vanilla options that can be modelled by class of…
Pricing financial or real options with arbitrary payoffs in regime-switching models is an important problem in finance. Mathematically, it is to solve, under certain standard assumptions, a general form of optimal stopping problems in…
We propose a time-adaptive, high-order compact finite difference scheme for option pricing in a family of stochastic volatility models. We employ a semi-discrete high-order compact finite difference method for the spatial discretisation,…
This paper presents a high-order deferred correction algorithm combined with penalty iteration for solving free and moving boundary problems, using a fourth-order finite difference method. Typically, when free boundary problems are solved…
An approach is treated for numerical integration of ordinary differential equations systems of the first order with choice of a computation scheme, ensuring the required local precision. The treatment is made on the basis of schemes of…
The purpose of this paper is to analyze and compute the early exercise boundary for a class of nonlinear Black--Scholes equations with a nonlinear volatility which can be a function of the second derivative of the option price itself. A…
This paper presents the solution to a European option pricing problem by considering a regime-switching jump diffusion model of the underlying financial asset price dynamics. The regimes are assumed to be the results of an observed pure…
This paper proposes a numerical method for pricing foreign exchange (FX) options in a model which deals with stochastic interest rates and stochastic volatility of the FX rate. The model considers four stochastic drivers, each represented…
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth-order accurate in space and second-order accurate in time. Under some restrictions, theoretical results…