We develop a new approach to approximating asset prices in the context of continuous-time models. For any pricing model that lacks a closed-form solution, we provide a closed-form approximate solution, which relies on the expansion of the intractable model around an “auxiliary” one. We...

We propose an iterative method for pricing American options under jump-diffusion models. A finite difference discretization is performed on the partial integro-differential equation, and the American option pricing problem is formulated as a linear complementarity problem (LCP). Jump-diffusion...

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 like unconditional stability in the sense of von Neumann...

New methods for solving general linear parabolic partial differential equations (PDEs) in one space dimension are developed. The methods combine quadratic-spline collocation for the space discretization and classical finite differences, such as Crank-Nicolson, for the time discretization. The...

Chen and Shen (2003) argue that it is possible to improve the Least Squares Monte Carlo Method (LSMC) of Longstaff and Schwartz (2001) to value American options by removing the least squares regression module. This would make not only faster but also more accurate. We demonstrate, using a large...

With the evolution of Graphics Processing Units (GPUs) into powerful and cost-efficient computing architectures, their range of application has expanded tremendously, especially in the area of computational finance. Current research in the area, however, is limited in terms of options priced and...

Is the American put option in the Black-Scholes model simply an incognito European one? In this paper, we develop a numerical procedure, in the context of the Black-Scholes model, to approximate the payoff of a European type option that generates prices that are equal to the prices of the...

We describe a broad setting under which, for European options, if the underlying asset form a geometric random walk then, the error with respect to the Black-Scholes model converges to zero at a speed of 1/n for continuous payoffs functions, and at a speed of 1/√n for discontinuous payoffs...

In this paper we introduce the CHEB method, a quadrature-based methodology for the fast and accurate pricing of European options with arbitrary payoffs. The method comes as a natural application of Chebfun, a numerical computing software package built on the approximation properties of Chebyshev...