Inside Volatility Arbitrage
Chapter One
The Volatility Problem
Suppose we use the standard deviation of possible future returns
on a stock as a measure of its volatility. Is it reasonable to take
that volatility as a constant over time? I think not.
-Fischer Black
INTRODUCTION
It is widely accepted today that an assumption of a constant volatility fails
to explain the existence of the volatility smile as well as the leptokurtic
character (fat tails) of the stock distribution. The above Fischer Black quote,
made shortly after the famous constant-volatility Black-Scholes model was
developed, proves the point.
In this chapter, we will start by describing the concept of Brownian
motion for the stock price return as well as the concept of historic volatility.
We will then discuss the derivatives market and the ideas of hedging and
risk neutrality. We will briefly describe the Black-Scholes partial derivatives
equation (PDE) in this section. Next, we will talk about jumps and level
dependent volatility models. We will first mention the jump diffusion process
and introduce the concept of leverage. We will then refer ... read full excerpt from Inside Volatility Arbitrage: The Secrets of Skewness ebook
