Univariate and Multivariate GARCH Models Applied to Bitcoin Futures Option Pricing

Eben Maré,Pierre J. Venter

doi:10.3390/jrfm14060261

Eben Maré, Pierre J. Venter

Open Access

https://doi.org/10.3390/jrfm14060261

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Abstract

In this paper, the Heston–Nandi futures option pricing model is applied to Bitcoin futures options. The model prices are compared to market prices to give an indication of the pricing performance. In addition, a multivariate Bitcoin futures option pricing methodology based on a multivatiate GARCH model is developed. The empirical results show that a symmetric model is a better fit when applied to Bitcoin futures returns, and also produces more accurate option prices compared to market prices for two out of three expiry dates considered.

Highlights

Cryptocurrencies, and especially Bitcoin, have received a lot of attention in the financial modelling literature in recent years
Research focusing on generalised autoregressive conditional heterskedasticty (GARCH) models applied to Bitcoin and Bitcoin derivative pricing is well documented in the literature
The results show that the hedge based on the bivariate GARCH model is the most reliable

Summary

Introduction

Cryptocurrencies, and especially Bitcoin, have received a lot of attention in the financial modelling literature in recent years. Modelling the historical returns of an asset as a univariate generalised autoregressive conditional heterskedasticty (GARCH) process is often used as a basis for price discovery in illiquid derivative markets. The model by Heston and Nandi (2000) is often used because it has a convenient closed-form solution This is usually applied to spot price dynamics. This model was extended to futures options on commodities by Li (2019a). We consider a modelling approach for price discovery in the Bitcoin futures spread option market. The approach is based on work by Rombouts and Stentoft (2011), who derived the risk-neutral dynamics of the spot price processes for a general class of multivariate heteroskedasticity models. The rest of this paper is structured as follows: Section 2 reviews the recent and relevant literature, Section 3 focuses on the theoretical framework (both univariate and mulitvariate options on Bitcoin futures), Section 4 presents the empirical results, and Section 5 provides concluding remarks

Literature Review

Theoretical Framework

Heston–Nandi Futures Option Pricing Model

Multivariate GARCH Futures Option Pricing Model

Multivariate GARCH Models

Empirical Results

Conclusions