Implied local volatility models

Abstract

This paper proposes data-driven “implied local volatility models” that are designed to fit the observed level, slope, convexity, and term-structure slope of implied volatility surface at any maturity and strike. The method of construction hinges on the Taylor structure of implied volatility under generic local volatility models and the formula of Dupire (1994). An empirical application to the S&P 500 index options data validates the stable performance of our method in and out of sample and triggers several economic interpretations before, during, and in the aftermath of COVID-19 pandemic. The flexibility of our method is further consolidated by the case study on fitting (ultra) short-maturity implied volatilities and concave implied volatility curves.