STOCHASTIC VOLATILITY MODELS FOR PRICING VIX OPTIONS CONSISTENT WITH VIX AND SPX IMPLIED VOLATILITIES: A SIMULATION APPROACH

Abstract

This thesis examines and compares the performance of two stochastic volatility models – the Heston model and the 3/2-model – in their abilities to price VIX options accurately while capturing the VIX and SPX implied volatility characteristics consistently. Through a simulation study, we find that the 3/2-model outperforms the Heston model in its ability to capture upward sloping VIX option implied volatility curves. Calibration of parameters confirms that the 3/2- model reflects market dynamics fairly well, and that the addition of jumps on the underlying index could potentially reduce pricing error. We implement three new ideas to the Heston model in an attempt to improve its ability to price VIX options.