Volatility smile dynamics

Abstract

‘Smile Dynamics’ is one of the key problems debated in the option smile literature today. It is a key component for consistent pricing of exotic options and hedging option portfolios. There exist various smile models which are convergent while pricing vanilla options. However, the values obtained by the models diverge when applied to exotic options and hedging strategies .These models are – Local Volatility, Jump Diffusion, Universal Volatility, Stochastic Volatility and other models. Smile Dynamics are classified as ‘sticky delta.' at one extreme and ‘sticky-strike at the other.They are classified on the basis of space homogeneity versus inhomogeneity.While local volatility models are in- homogeneous, simple stochastic volatility models are homogeneous.In order to effectively control and predict smile dynamics, one can either reintroduce some degree of in- homogeneity or propose a mixture of models.