Ďuriš, Karol, Tan, Shih-Hau, Lai, Choi-Hong ORCID: https://orcid.org/0000-0002-7558-6398 and Ševčovič, Daniel (2016) Comparison of analytical approximation formula and Newton's method for solving a class of nonlinear Black-Scholes parabolic equations. Computational Methods in Applied Mathematics, 16 (1). pp. 35-50. ISSN 1609-4840 (Print), 1609-9389 (Online) (doi:10.1515/cmam-2015-0035)

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Abstract

Market illiquidity, feedback effects, presence of transaction costs, risk from unprotected portfolio and other nonlinear effects in PDE-based option pricing models can be described by solutions to the generalized Black–Scholes parabolic equation with a diffusion term nonlinearly depending on the option price itself. In this paper, different linearization techniques such as Newton’s method and the analytic asymptotic approximation formula are adopted and compared for a wide class of nonlinear Black–Scholes equations including, in particular, the market illiquidity model and the risk-adjusted pricing model. Accuracy and time complexity of both numerical methods are compared. Furthermore, market quotes data was used to calibrate model parameters.

Item Type:	Article
Uncontrolled Keywords:	Nonlinear PDE, Asymptotic Formula, Newton's Method, Finite Difference Method, Option Pricing, Black–Scholes Equation
Faculty / School / Research Centre / Research Group:	Faculty of Engineering & Science > School of Computing & Mathematical Sciences (CMS)
Last Modified:	30 Apr 2020 10:16
URI:	http://gala.gre.ac.uk/id/eprint/14897

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