Pricing perpetual American options under multiscale stochastic elasticity of variance

•We study the effects of the stochastic elasticity of variance on perpetual American option.•Our SEV model consists of a fast mean-reverting factor and a slow mean-revering factor.•A slow scale factor has a very significant impact on the option price.•We analyze option price structures through the market prices of elasticity risk.

This paper studies pricing the perpetual American options under a constant elasticity of variance type of underlying asset price model where the constant elasticity is replaced by a fast mean-reverting Ornstein–Ulenbeck process and a slowly varying diffusion process. By using a multiscale asymptotic analysis, we find the impact of the stochastic elasticity of variance on the option prices and the optimal exercise prices with respect to model parameters. Our results enhance the existing option price structures in view of flexibility and applicability through the market prices of elasticity risk.