Advanced model calibration on bitcoin options

Abstract

In this paper, we investigate the dynamics of the bitcoin (BTC) price through the vanilla options available on the market. We calibrate a series of Markov models on the option surface. In particular, we consider the Black-Scholes model, Laplace model, five variance gamma-related models and the Heston model. We examine their pricing performance and the optimal risk-neutral model parameters over a period of 2 months. We conclude with a study of the implied liquidity of BTC call options, based on conic finance theory.

Cryptocurrency volatility markets

“…Madan et al. ( 2019 ) provide such a study for cryptocurrency options. For the purpose of a volatility index, however, it is paramount that the only information extracted, i.e., the only free parameter in the model, is implied volatility.…”

Price discovery in the cryptocurrency option market: A univariate GARCH approach

“…Therefore, cryptoccurency derivative prices are dependent on cryptocurrency prices. Madan et al (2019) explain that the cryptocurrency derivatives market is a young market and therefore different pricing methodologies are required for price discovery. Madan et al (2019) found that models that incorporate stochastic volatility generally perform well when applied to the pricing of cryptocurrency options.…”

Theory of Cryptocurrency Interest Rates

“…where ξ t = (X t − a 0 , Y t − b 0 , Z t − c 0 ) and δ = (a 1 , b 1 , c 1 ). It turns out that the calculation leading to (27) is applicable for complex parameters a, b, and c. To see this, we perform the integration explicitly. Recall that in the real case where δ = 0 we have one fixed vector ξ t in the exponent of the integrand, so by using the spherical symmetry we choose this vector to point in the z direction, resulting in the simple expression R · ξ t = Rξ t cos θ, which was used in the calculation of (27).…”