Modeling volatility smile: Empirical evidence from India

Abstract

The objective of this article is twofold. The first and foremost objective is to investigate the information content of the volatility smile and to model its parabolic smile/skew pattern having advance quadratic formulations, to serve the best of requirements of derivative and capital market. The second relative objective is to find out the impeccable option pricing model capable of expanding the smile/smirk phenomenon of Black–Scholes, which can meet the requirements of option traders and practitioners, specifically during the period of high financial flux as capital market is subject to high unpredictability and may continue to be so. For modeling the volatility smile, we have identified a set of traditional Deterministic Volatility Functions (DVFs) of Dumas et al (1998), and endeavored in restructuring and redesigning of DVFs and further analytically examining the empirical effect of it. The underlying focus of this article remains to emphasize on the analytical investigation of the parameters of DVF models and its relative performance with respect to the classical Black–Scholes model. Furthermore, to search the most apt DVF model that could emerge as the most potential framework for the prediction of volatility smile and the market option price, this article utilizes the data of the most turbulent recent period of Indian and world economy, year 2007–2009, and finds the practical implications of hypothecated DVF models during the uncertain upheavals of financial forces.