We are the first to study the pricing and hedging of VIX options via Monte Carlo (MC) under GARCH(1,1) and Glosten–Jagannathan–Runkle GARCH(1,1) models. Our pricing is ab initio and out‐of‐sample and can be implemented in real time. Importantly, we propose the so‐called single‐option...

This paper assesses variance risk premium and forecasts out-of-sample VIX under GARCH(1,1), GJR, and Heston-Nandi models. With the date-t GARCH parameters estimated in a moving window fashion from 3,500 daily returns of the S&P 500 index, a hypothetical date-t VIX turns out to be below the...

Known discrete dollar dividends lead to non-recombining binomial trees (NR-BT) with an explosion of nodes, which are more difficult to implement and much less efficient. This paper proposes a method for constructing a recombining binomial tree via balanced dividend adjustments (BDA). BDA splits...

Zhu and Lian (Journal of Futures Markets, 2012) proposed the first closed-form formulas for VIX futures prices, whihch are conceptually appealing and easy to implement. Unfortunately, the paper is found to contain three kinds of errors. The main formula (9) for the price of futures misses the...

The authors propose the first closed-form price formulas for VIX futures under the widely used discrete-time symmetric GARCH(1, 1) and asymmetric Glosten–Jagannathan–Runkle (GJR) GARCH(1, 1) models. For VIX futures expired before July 21, 2017, the proposed methods, which are truly simple,...