). This transformation adjusts the moneyness coordinate of the implied volatility smile in an attempt to remove the … indicate that in a statistical sense there remains a possibility that the implied volatility smiles are still not the same … utilizes the dynamic structure of implied volatility surface allowing out-of-sample forecasting and information on unleveraged …

volatility smiles. We model leveraged and inverse ETF option prices using partial differential equations (PDEs) and determine …

empirical data the implied volatility skews for LETF options based on the S&P 500. In order to enhance their comparison with non … between leveraged and unleveraged ETFs. Under a multiscale stochastic volatility framework, we apply asymptotic techniques to … derive an approximation for both the LETF option price and implied volatility. The approximation formula reflects the role of …