An efficient numerical method for pricing American put options under the CEV model

The constant elasticity of variance (CEV) model is a practical approach to option pricing by fitting to the implied volatility smile. However, pricing American options is computationally intensive because no analytical formulas are available. In this paper, we present numerical methods to find the o...

Full description

Saved in:
Bibliographic Details
Published in:Journal of computational and applied mathematics 2021-06, Vol.389, p.113311, Article 113311
Main Author: Lee, Jung-Kyung
Format: Article
Language:English
Subjects:
American option
Constant elasticity of variance model
Cubic spline interpolation
Optimal exercise boundary
Transformed function
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The constant elasticity of variance (CEV) model is a practical approach to option pricing by fitting to the implied volatility smile. However, pricing American options is computationally intensive because no analytical formulas are available. In this paper, we present numerical methods to find the optimal exercise boundary with respect to an American put option under the CEV model. This problem corresponds to the free boundary (also called an optimal exercise boundary) problem for a partial differential equation. We use a transformed function that has Lipschitz character near the optimal exercise boundary to determine the optimal exercise boundary. After determining the optimal exercise boundary, we calculate American put option values under the CEV model using the finite-difference method. Finally, we use the proposed numerical method to obtain several results that are then compared with the results of other methods.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2020.113311