The efficacy of affine jump-diffusion stochastic volatility models for bitcoin option pricing

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School of Business | Master's thesis
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The current state of literature on Bitcoin option pricing is yet to evolve from its adolescence phase, marked by a discernible void concerning the paucity of comprehensive empirical studies addressing the predictive power of stochastic volatility models that incorporate two contemporaneous and correlated jump components. This gap serves as the impetus for the investigation into this obscure terrain. The Bitcoin option market exhibits a distinctive profile characterized by extreme volatility, non-stationarity, and an inherent proclivity for frequent discontinuities. These unique attributes pose challenges in accurately modeling option prices, necessitating the utilization of sophisticated models to improve model fit. This paper endeavors to fill this academic vacuum by assessing the fidelity of stochastic models in replicating volatility skews. Specifically, it employs a stochastic simulation scheme to investigate the efficacy of a state-of-the-art jump-diffusion model –known as SVCJ (stochastic volatility with correlated jumps) – in comparison with its nested counterparts. The auxiliary objective is determining which classifications of maturity-moneyness show inferior performance for said model. Empirical results indicate that the SVCJ model substantially outperforms its counterparts in both the calibration and validation periods. Maturity-moneyness classifications underscore its superiority, shown by exhibiting the lowest root mean squared errors for 64% of the categories. It is also documented that its forecasting accuracy is attenuated for shorter-dated options. The outcome demonstrates that modeling with two jump components leads to a significant improvement-of-fit in explaining the volatility surface. Thus, this double-jump feature is crucial in capturing sudden meteoric surges and nose-dives with greater accuracy.
Thesis advisor
Nyberg, Peter
stochastic volatility models, bitcoin option pricing, SVCJ, calibration, option pricing models
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