Conditional Volatility and the GARCH Option Pricing Model with Non-Normal Innovations

Forecasting VIX Using Filtered Historical Simulation

“…To distinguish from the spot variance under the physical measure σ 2 t , the risk-neutral variance is denoted by σ * 2 t . Whilst Barone-Adesi et al (2008) assume that the spot variance is the same under the physical and risk-neutral measures, Byun and Min (2013) show that a model provides more accurate pricing performance by allowing the risk-neutral spot variance to be different from the physical one. Also, Kanniainen et al (2014) demonstrate that extracting the spot volatility from the VIX index can improve on the model's performance compared with calculating spot volatility using the series of the underlying asset returns.…”

“…Also, several studies use GARCH estimates to forecast VIX as an extended application of GARCH pricing models; see, for instance, Barone-Adesi et al (2008) and Byun and Min (2013). Other related articles include Kambouroudis and McMillan (2016) who consider VIX as an exogenous variable within a selection of GARCH models, and Huang et al (2019) who estimate the extended leverage heterogeneous autoregressive gamma (LHARG) model of Majewski et al (2015) using both the VIX term structure and VIX futures.…”

“…Following Barone-Adesi et al (2008), we allow the volatility parameters to be different under the physical and risk-neutral measures. Byun and Min (2013) point out that using the same values for the one-day-ahead conditional volatility under both measures, as in Barone-Adesi et al (2008), will lead to poor empirical performance. Therefore, in this paper, we consider the volatility processes to be different under the two measures.…”

“…Byun and Min (2013) show that, instead of just simply improving the goodness of fit, the estimated spot variance can be treated as the true spot variance under the risk-neutral measure.9 In this study, we use the trading day count convention, as the innovation distribution is estimated with trading days returns.10 BothBarone-Adesi et al (2008) andByun and Min (2013) calibrate risk-neutral GARCH parameters using a cross-section of option prices, producing 20,000 and 50,000 simulation paths, respectively.11 The starting dates of VIX, VIX3M and VIX6M are 2 January 2004, 4 December 2007 and 7 January 2008, respectively.12 We follow the same criteria ofBarone-Adesi et al (2008) to sort data: (1) only use the out-of-themoney European options since they are more actively traded than in-the-money options. (2) choose options which mature in more than 10 days and less than 360 days.…”

Accelerating FHS Option Pricing Under Linear GARCH

“…Christoffersen et al (2010) show that excess skewness and kurtosis drive a wedge between physical and risk-neutral one-day-ahead conditional volatilities; (2) Monte Carlo simulation technique is used in FHS method, which is very time-consuming and suffers from random sampling errors. The first problem has been discussed in Byun and Min (2013). This paper attempts to tackle the second problem.…”