Calibration Strategies of Stochastic Volatility Models for Option Pricing

This study examines how calibrated stochastic volatility models maintain their option pricing performance over subsequent days. Specifically, using a number of sets of single and multi-day data, different loss functions, and regularization techniques, we examine the dynamics of the pricing errors of two well-recognized stochastic volatility models. We find that, depending on the loss function, the use of multi-day data in calibration can slow down the increase in the pricing error for long-maturity options. On the other hand, the calibration with 1 day of data tends to give the smallest in-sample error diminishing the benefit of larger multi-day datasets. Differences between different sizes of datasets are more noticeable with the discrete-time volatility model than a continuous time one but in both cases 1 day of data would be the optimal choice and in most cases daily calibration is needed