CEV Asymptotics of American Options
Journal of Mathematical Analysis and Applications. 403, 451-463
31 Pages Posted: 23 Jun 2020
Date Written: March 5, 2013
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
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