Inside Volatility Filtering: Secrets of the Skew, 2nd Edition

Introduction (First Edition)

Summary

This book focuses on developing Methodologies for Estimating Stochastic Volatility (SV) parameters from the Stock-Price Time-Series under a Classical framework. The text contains three chapters and is structured as follows:

In the first chapter, we shall introduce and discuss the concept of various parametric SV models. This chapter represents a brief survey of the existing literature on the subject of nondeterministic volatility.

We start with the concept of log-normal distribution and historic volatility. We then will introduce the Black-Scholes [40] framework. We shall also mention alternative interpretations as suggested by Cox and Rubinstein [71]. We shall state how these models are unable to explain the negative-skewness and the leptokurticity commonly observed in the stock markets. Also, the famous implied-volatility smile would not exist under these assumptions.

At this point we consider the notion of level-dependent volatility as advanced by researchers such as Cox and Ross [69, 70] as well as Bensoussan, Crouhy, and Galai [34]. Either an artificial expression of the instantaneous variance will be used, as is the case for Constant Elasticity Variance (CEV) models, or an implicit expression will be deduced from a Firm model similar to Merton's [199], for instance.

We also will bring up the subject of Poisson Jumps [200] in the distributions providing a negative-skewness and larger kurtosis. These jump-diffusion models offer a link ...