CEV Asymptotics of American Options

Journal of Mathematical Analysis and Applications. 403, 451-463

31 Pages Posted: 23 Jun 2020

See all articles by Chi Seng Pun

Chi Seng Pun

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences

Hoi Ying Wong

The Chinese University of Hong Kong (CUHK) - Department of Statistics

Date Written: March 5, 2013

Abstract

The constant elasticity of variance (CEV) model is a practical approach to option pricing by fitting to the implied volatility smile. Its application to American-style derivatives, however, poses analytical and numerical challenges. By taking the Laplace-Carson transform (LCT) to the free-boundary value problem characterizing the option value function and the early exercise boundary, the analytical result involves confluent hyper-geometric functions. Thus, the numerical computation could be unstable and inefficient for certain set of parameter values. We solve this problem by an asymptotic approach to the American option pricing problem under the CEV model. We demonstrate the use of the proposed approach using perpetual and finite-time American puts.

Keywords: CEV model, American options, Partial differential equation, Perturbation technique

Suggested Citation

Pun, Chi Seng and Wong, Hoi Ying, CEV Asymptotics of American Options (March 5, 2013). Journal of Mathematical Analysis and Applications. 403, 451-463, Available at SSRN: https://ssrn.com/abstract=3613747

Chi Seng Pun (Contact Author)

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences ( email )

SPMS-MAS-05-22
21 Nanyang Link
Singapore, 637371
Singapore
(+65) 6513 7468 (Phone)

HOME PAGE: http://personal.ntu.edu.sg/cspun/

Hoi Ying Wong

The Chinese University of Hong Kong (CUHK) - Department of Statistics ( email )

Shatin, N.T.
Hong Kong

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