Empirical performance of rough volatility models in the KOSPI 200 options market using deep surrogates

This study provides a systematic comparison of the pricing performance of the rough volatility models—rBergomi and rHeston—with that of classical one-factor stochastic volatility (SV) and stochastic volatility jump-diffusion (SVJ) models in the KOSPI 200 index options market. Using an extensive daily option dataset spanning the 22 years from 2003 to 2025, we conduct daily calibration and out-of-sample forecasting experiments. To overcome the computational bottleneck of rough volatility models and to place all models in a uniform comparison environment, we adopt the deep surrogate methodology, which replaces the pricing function with a deep neural network and delivers calibration at effectively real-time speed. In terms of in-sample pricing fit, the SVJ models with eight to nine parameters perform best, but the rBergomi model, which has only three core parameters, is not far behind. Out-of-sample, by contrast, the forecasting accuracy of the SVJ models deteriorates sharply because of parameter overfitting, whereas rBergomi dominates at every forecast horizon. The estimated Hurst exponents lie mostly between 0 and 0.5, confirming that the roughness of volatility is present in the KOSPI 200 options market under the risk-neutral measure as well. To our knowledge, this is the first study to apply rough volatility models to KOSPI 200 option pricing and compare them systematically with classical models. The results demonstrate the strength of rough volatility models, which capture a complex implied volatility structure and maximize forecasting power with only a handful of parameters, and the practical viability of the deep surrogate methodology.