Modeling SSE 50 ETF Returns and Option Pricing: Evidence from a Score-Driven GARCH-Jump Approach

Modeling stock returns and option prices in the presence of jumps remains a central challenge in financial economics. This paper employs a novel score-driven GARCH-jump model to analyze SSE 50 ETF returns and option pricing. The main findings are as follows. First, we use 50 ETF spot returns to estimate historical volatility and jump intensity, and find that the SDSDJ (Score-driven separate dynamic jumps) model significantly outperforms conventional GARCH-jump models in model fitting. Second, we evaluate both in-sample and out-of-sample pricing performance using 50 ETF options data, and find that the SDSDJ model achieves the lowest in-sample pricing error among all benchmarks, while its simplified variant — the SDJ (Score-driven jumps) model — delivers the most accurate out-of-sample results. Third, the superior pricing performance of both models is robust across different levels of moneyness and days-to-maturity (DTM).