Options valuation and calibration for leveraged exchange-traded funds with Heston–Nandi and inverse Gaussian GARCH models

Abstract

Leveraged exchange-traded funds (LETF) are newly introduced ETFs that have become increasingly popular. It closely tracks the value of an underlying index while allowing for additional leverage. In this paper, we consider the valuation of options written on LETF under two popular affine GARCH models, the Heston–Nandi model and the inverse Gaussian GARCH model. We also calibrate the two models using market data, and demonstrate the superior pricing performance.