Hybrid Volatility Modeling with Calibration Under Structural Price Features for Option Pricing in Cryptocurrency Markets

Abstract

The classical option pricing frameworks may be inefficient in the cryptocurrency market due to its characteristics of persistent volatility clustering, heavy-tailed return distributions, and structural price dynamics. This paper introduces a hybrid model that incorporates the econometric and deep learning models to estimate implied volatil- ity for option pricing in the cryptocurrency market. In the framework of the hybrid model, the Student-t GARCH model and the Long Short-Term Memory (LSTM) model are used to capture the conditional volatility dy- namics and learn the nonlinear temporal dependencies in realized volatility, respec- tively. The expected realized volatility proxy generated by the hybrid model is cali- brated to market-implied volatility with the incorporation of structural features derived from Fibonacci retracement levels, which explain variations in volatility risk premiums of option prices. Using cryptocurrency options data and corresponding market-implied volatility ob- servations, the empirical analysis shows that the calibrated volatility proxy is sig- nificantly related to market-implied volatility. Moreover, the inclusion of structural features improves the interpretation of the volatility gap between model-implied and market-implied measures. Additionally, the calibrated proxy, when embedded in the Black–Scholes framework, produces economically meaningful option prices. Overall, the findings support the view that a hybrid volatility-modeling approach, augmented by structural market features, provides a useful framework for cryptocurrency option valuation and volatility-premium analysis.