Prediction-based estimating functions for stochastic volatility models with noisy data: comparison with a GMM alternative

摘要

Prediction-based estimating functions (PBEFs), introduced in Sorensen (Econom J 3:123-147, 2000), are reviewed, and PBEFs for the Heston (Rev Financ Stud 6:327-343, 1993) stochastic volatility model are derived with and without the inclusion of noise in the data. The finite sample performance of the PBEF-based estimator is investigated in a Monte Carlo study and compared to the performance of the Generalized Method of Moments (GMM) estimator from Bollerslev and Zhou (J Econom 109: 33-65, 2002) that is based on conditional moments of integrated variance. We derive new moment conditions in the presence of noise, but we also consider noise correcting the GMM estimator by basing it on a realized kernel instead of realized variance. Our Monte Carlo study reveals great promise for the estimator based on PBEFs. The study also shows that the PBEF-based estimator outperforms the GMM estimator, both in the setting with MMS noise and in the setting without MMS noise, especially for small sample sizes. Finally, in an empirical application we fit the Heston model to SPY data and investigate how the two methods handle real data and possible model misspecification. The empirical study also shows how the flexibility of the PBEF-based method can be used for robustness checks.