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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 follows. We then explore the problem of pricing American options with the Runge-Kutta-Legendre scheme under the one factor Black-Scholes and the two factor Heston stochastic volatility models, as well as the pricing of butterfly spread and digital options under the uncertain volatility model, where a Hamilton-Jacobi-Bellman partial differential equation needs to be solved. We explore the order of convergence in these problems, as well as the option greeks stability, compared to the literature and popular schemes such as Crank-Nicolson, with Rannacher time-stepping.
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 coupled with H
We continue a series of papers devoted to construction of semi-analytic solutions for barrier options. These options are written on underlying following some simple one-factor diffusion model, but all the parameters of the model as well as the barrie
In this paper we propose two efficient techniques which allow one to compute the price of American basket options. In particular, we consider a basket of assets that follow a multi-dimensional Black-Scholes dynamics. The proposed techniques, called G
We present new numerical schemes for pricing perpetual Bermudan and American options as well as $alpha$-quantile options. This includes a new direct calculation of the optimal exercise barrier for early-exercise options. Our approach is based on the
The main objective of this paper is to present an algorithm of pricing perpetual American put options with asset-dependent discounting. The value function of such an instrument can be described as begin{equation*} V^{omega}_{text{A}^{text{Put}}}(s) =