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Volatility as an Asset Class

Obvious Benefits and Hidden Risks

Series:

Juliusz Jabłecki, Ryszard Kokoszczyński, Paweł Sakowski, Robert Ślepaczuk and Piotr Wójcik

Volatility derivatives are an important group of financial instruments and their list is much longer than volatility index futures and options. This book reviews methods used for measurement, estimation and forecasting volatility and presents major classes of volatility derivatives and their possible applications in investment strategies and portfolio optimization. Since volatility is not constant, its term structure and the phenomenon of the volatility risk premium are discussed in view of the permanently instable relation between realized and implied volatility. The study proposes a method to use this information in the process of forecasting future values of volatility.
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1 Volatility and Its Estimation

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1.1 Introduction

Volatility cannot be directly observed – this notwithstanding it is one of the most important variables in finance. Usually, we associate volatility with the spread of asset returns, so statistically volatility could be measured as variance or standard deviation of the respective sample. However, this is not the only possible approach to this question. The abundant literature on volatility may be classified into two streams. The first one addresses the issue of volatility from a statistical or econometric perspective. The second stream focuses on possible financial applications: asset allocation, risk management, and asset pricing8. Both streams are interrelated within the theory of option pricing in a way we present below.

Black, Scholes and Merton, the founding fathers of this theory, brilliantly notice that options are not independent instruments and can be replicated with less complex instruments. The following example illustrates this clearly: Call option for, say, IBM stock increases its value with stock price going up. Naturally, that directional exposure can be hedged by a short sale of some number of IBM shares. More generally, to hedge against the linear part of exposure represented by option C one is required to take an opposite position in units of underlying instrument S. In other words, a portfolio consisting of a long position in call option and a short position in adequate number of shares is locally free of risk. This intuitive reasoning may be formalized (taking into account time, financing costs and no-arbitrage condition)...

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