Abstract
The N-body problem is an active research topic in physics for which there are two major algorithms for efficient computation, the fast multipole method and treecode, but these algorithms are not popular in financial engineering. In this article, we apply a fast N-body algorithm called the Cartesian treecode to the computation of the integral operator of integro-partial differential equations to compute option prices under the CGMY model, a generalization of a jump-diffusion model. We present numerical examples to illustrate the accuracy and effectiveness of the method and thereby demonstrate its suitability for application in financial engineering.
Highlights
The standard and celebrated model for option pricing in the financial industry has been the Black-Scholes model [1] because of its simplicity
We apply a fast N-body algorithm called the Cartesian treecode to the computation of the integral operator of integro-partial differential equations to compute option prices under the CGMY model, a generalization of a jump-diffusion model
We examine its computational accuracy and ease of implementation for the computation of the integral operators of the partial integro-differential equations (PIDEs)
Summary
The standard and celebrated model for option pricing in the financial industry has been the Black-Scholes model [1] because of its simplicity. For a European option, researchers have suggested efficient schemes which apply numerical methods such as the fast Fourier transform (FFT) [3], the Hilbert transform [4], and the Fourier-cosine (COS) [5] methods. The application of these methods to path-dependent options has been investigated (for example, [6]). One application of FMM called the fast Gauss transform (FGT, [16]) has been implemented under Merton’s jump-diffusion model [19] to solve the corresponding PIDE [9]. We examine whether treecode is applicable in the field of financial engineering
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