Pricing Options with the Stochastic Volatility Regime Simulation for GARCH, HAR GARCH-VIX and VIX Models

Abstract

This working paper uses as a starting point the filtered historical simulation (FHS) approach developed by Barone-Adesi et al. One builds a GJR-GARCH model and generates Monte-Carlo return/price paths with normalized returns. This introduces a severe drift-bias. The Stochastic Volatility Regime Simulation (SVRS) avoids the bias by sampling from the same volatility regime. As an alternative to GJR-GARCH an asymmetric HAR and a GARCH-VIX model is used. Path sampling is done in the same way. As a model free alternative a VIX based approach is additionally investigated. This alternative clearly beats the models during the pre and post-Brexit market turmoil. Barone-Adesi et al. transform the real-world into the risk-neutral measure. The current model stays in the real-measure. One simulates a realistic trading behavior by hedging the options along the Monte-Carlo paths. One can calibrate the model by adding external noise.