A Simulation Methodology Consistent with the Prices of Plain Vanilla, One Touch and VIX Options

Abstract

In this paper, we consider how to generate simulation paths for underlying asset price and volatility that reproduce the volatility smiles of plain vanilla, one touch and VIX options. Unlike general volatility models, we propose a method using a Markov functional model that uses the realized volatility of the underlying asset price as the driver of VIX fluctuation, instead of using the VIX fluctuation as a random variable independent of the underlying asset price. We show that this model can generate simulation paths of underlying asset price and volatility that reproduces these volatility smiles.

Keywords: Markov Functional Model, Volatility Smile, SPX/VIX problem, Touch Option, VIX Option, Variance Risk Premium, Historical Simulation

JEL Classification: G12,G13