Multiscale analysis of a perpetual American option with the stochastic elasticity of variance

A perpetual American option is considered under a generalized model of the constant elasticity of variance model where the constant elasticity is perturbed by a small fast mean-reverting Ornstein–Uhlenbeck process. By using a multiscale asymptotic analysis, we find the impact of the stochastic elasticity of variance on option prices as well as optimal exercise prices. Our results improve the existing option price structure in view of flexibility and applicability through the market price of risk. The revealed results may provide useful information on real option problems.