A Hybrid Monte Carlo and Finite Difference Method for Option Pricing

Darae Jeong, Minhyun Yoo, Changwoo Yoo and Junseok Kim ()
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Darae Jeong: Korea University
Minhyun Yoo: Korea University
Changwoo Yoo: Korea University
Junseok Kim: Korea University

Computational Economics, 2019, vol. 53, issue 1, No 5, 124 pages

Abstract: Abstract We propose an accurate, efficient, and robust hybrid finite difference method, with a Monte Carlo boundary condition, for solving the Black–Scholes equations. The proposed method uses a far-field boundary value obtained from a Monte Carlo simulation, and can be applied to problems with non-linear payoffs at the boundary location. Numerical tests on power, powered, and two-asset European call option pricing problems are presented. Through these numerical simulations, we show that the proposed boundary treatment yields better accuracy and robustness than the most commonly used linear boundary condition. Furthermore, the proposed hybrid method is general, which means it can be applied to other types of option pricing problems. In particular, the proposed Monte Carlo boundary condition algorithm can be implemented easily in the code of the existing finite difference method, with a small modification.

Keywords: Black–Scholes equation; Finite difference method; Option pricing; Boundary condition; Monte Carlo simulation (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10614-017-9730-4

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