<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, we present an intelligent combination of partition of unity (PU) and finite element (FE) methods for valuing American option pricing problems governed by the Black-Scholes (BS) model. The model is based on a partial differential equation (PDE) from which one can deduce the Black-Scholes formula, which gives a theoretical estimated value of options using current stock prices, expected dividends, the option’s strike price, expected interest rates, time to expiration and expected volatility. Although the finite element method (FEM) seems to be an alternative tool for pricing options with a few applications reported in the literature, this combination called the Partition of Unity Finite Element Method (PUFEM) appears to offer many of the desired properties. The main advantage of the proposed approach is its ability to locally refine the solution by adapting an incorporated specific class of enrichment in the finite element space instead of generating a new fine mesh for the problem under study. Numerical computations are carried out to show a huge reduction in the number of degrees of freedom required to achieve a fixed accuracy which confirms that the PUFE method used is very efficient and gives better accuracy than the conventional FE method.</p>
</abstract>

In this paper, we present an intelligent combination of partition of unity (PU) and finite element (FE) methods for valuing American option pricing problems governed by the Black-Scholes (BS) model. The model is based on a partial differential equation (PDE) from which one can deduce the Black-Scholes formula, which gives a theoretical estimated value of options using current stock prices, expected dividends, the option’s strike price, expected interest rates, time to expiration and expected volatility. Although the finite element method (FEM) seems to be an alternative tool for pricing options with a few applications reported in the literature, this combination called the Partition of Unity Finite Element Method (PUFEM) appears to offer many of the desired properties. The main advantage of the proposed approach is its ability to locally refine the solution by adapting an incorporated specific class of enrichment in the finite element space instead of generating a new fine mesh for the problem under study. Numerical computations are carried out to show a huge reduction in the number of degrees of freedom required to achieve a fixed accuracy which confirms that the PUFE method used is very efficient and gives better accuracy than the conventional FE method.

A Partition of unity finite element method for valuation American option under Black-Scholes model

Engineering Sciences and Energy Management Laboratory

Laboratory of Engineering Sciences, Faculty of Science

Technical Research Laboratory, Faculty of Applied Sciences

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

In this paper, we present an intelligent combination of partition of unity (PU) and finite element (FE) methods for valuing American option pricing problems...

A Partition of unity finite element method for valuation American option under Black-Scholes model

Published Online: Jan 29, 2021

Page range: 324 - 336

Received: Aug 30, 2020

Accepted: Jan 20, 2021

DOI: https://doi.org/10.2478/mjpaa-2021-0021

Keywords
American option, Black-Scholes, Finite element method, Enriched finite element method

© 2021 Zaineb El kharrazi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

A Partition of unity finite element method for valuation American option under Black-Scholes model

Published Online: Jan 29, 2021

Page range: 324 - 336

Received: Aug 30, 2020

Accepted: Jan 20, 2021

DOI: https://doi.org/10.2478/mjpaa-2021-0021

KeywordsAmerican option, Black-Scholes, Finite element method, Enriched finite element method

© 2021 Zaineb El kharrazi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
American option, Black-Scholes, Finite element method, Enriched finite element method