Monotonicity of implied volatility for perpetual put options - Ekström, Erik; Mellquist, Ebba (Journal of applied probability, 2024)
We define and study properties of implied volatility for American perpetual put options. In particular, we show that if the market prices are derived from a local volatility model with a monotone volatility function, then the corresponding implied volatility is also monotone as a function of the strike price.