Option-implied filtering: evidence from the GARCH option pricing model

Univariate and Multivariate GARCH Models Applied to Bitcoin Futures Option Pricing

“…The overall purpose was the pricing of crude oil futures options. Li (2019a) concludes that optionimplied filtering is superior when compared to futures-based filtering when pricing crude oil futures options. Li (2019b) also applied the model to natural gas futures.…”

“…Limited research has focused on the GARCH option pricing model applied to futures options. Li (2019a) extended the Heston-Nandi model to futures options. The overall purpose was the pricing of crude oil futures options.…”

“…The model by Heston and Nandi (2000) is widely used in the literature for the pricing of vanilla options. This model was extended to futures options by Li (2019a), who applied the model to crude oil futures. The futures dynamics under the real-world measure P are given by (Li 2019b):…”

“…, where γ * = γ + λ. Given the risk-neutral dynamics, a closed-form formula for a European call option on a futures contract can be obtained, see Li (2019a) for more detail. The parameters are estimated using maximum likelihood estimation; the log-likelihood function is given by (Wang et al 2017):…”

“…However, this is usually applied to spot price dynamics. This model was extended to futures options on commodities by Li (2019a). The Chicago Mercantile Exchange (CME) was the first established exchange to launch Bitcoin futures options in the first quarter of 2020 (Bharadwaj 2021).…”