# Volatility as an Asset Class

## Obvious Benefits and Hidden Risks

#### Series:

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

### Book (EPUB)

- ISBN:
- 9783653978841

- Availability:
- Available

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## Prices

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- Frankfurt am Main, Berlin, Bern, Bruxelles, New York, Oxford, Wien, 2015. 178 pp., 36 tables, 49 graphs

- Cover
- Title
- Copyright
- About the author(s)/editor(s)
- About the book
- This eBook can be cited
- Contents
- Introduction
- 1.1 Introduction
- 1.2.1 Alternative volatility estimators
- 1.2.2 High-frequency data
- 1.2.3 Concluding remarks
- 1.3.1 Time series analysis
- 1.3.2 Forecasts implied by option prices
- 1.3.3 Concluding remarks
- 1.4.1 Local volatility model
- 1.4.2 Stochastic volatility models
- 1.4.3 Concluding remarks
- 1.5 Conclusions
- 2.1 Volatility exposure in a delta-hedged option
- 2.2 Variance swaps
- 2.3 VIX and VIX futures
- 2.4 VIX options
- 2.5 The economics of volatility derivatives
- 3.1 Introduction
- 3.2 Options as volatility instruments – replicating realized volatility
- 3.3 Volatility arbitrage based on various frequencies of data
- 3.4 Methodology and data
- 3.5.1 S&P500 index – the most developed market
- 3.5.2 The case for other developed markets (FTSE, NIKKEI225, DAX)
- 3.5.3 The case for emerging markets (WIG20, KOSPI, BOVESPA) ...
- 3.6 Summary
- 4.1 Introduction
- 4.2 The merits of investing in volatility
- 4.3.1 Benchmark portfolio
- 4.3.2 Long position in implied volatility
- 4.3.3 Short position in realized volatility
- 4.3.4 A combination of long and short position in volatility
- 4.4 Summary
- 5.1 Introduction
- 5.2 Volatility as a traded asset
- 5.3 Markowitz model – a short review 101
- 5.4 Black-Littermann model – a short review
- 5.5.1 Data used
- 5.5.2 Simulation
- 5.5.3 Empirical results
- 5.6.1 Data used
- 5.6.2 Simulation
- 5.6.3 Empirical results
- 5.7 Summary
- 6.1 Introduction
- 6.2.1 Motivation
- 6.2.2 Literature review
- 6.2.3 Methodology and data
- 6.2.4 Results
- 6.2.5 Remarks
- 6.3.1 Motivation
- 6.3.2 Data description
- 6.3.3 Methodology
- 6.3.4 Measures of volatility term structure
- 6.3.5 Forecasting properties of volatility term structure
- 6.3.6 Investment model
- 6.4 Summary
- Conclusions
- List of figures
- List of tables
- Bibliography
- Cover
- Title
- Copyright
- About the author(s)/editor(s)
- About the book
- This eBook can be cited
- Contents
- Introduction
- 1.1 Introduction
- 1.2.1 Alternative volatility estimators
- 1.2.2 High-frequency data
- 1.2.3 Concluding remarks
- 1.3.1 Time series analysis
- 1.3.2 Forecasts implied by option prices
- 1.3.3 Concluding remarks
- 1.4.1 Local volatility model
- 1.4.2 Stochastic volatility models
- 1.4.3 Concluding remarks
- 1.5 Conclusions
- 2.1 Volatility exposure in a delta-hedged option
- 2.2 Variance swaps
- 2.3 VIX and VIX futures
- 2.4 VIX options
- 2.5 The economics of volatility derivatives
- 3.1 Introduction
- 3.2 Options as volatility instruments – replicating realized volatility
- 3.3 Volatility arbitrage based on various frequencies of data
- 3.4 Methodology and data
- 3.5.1 S&P500 index – the most developed market
- 3.5.2 The case for other developed markets (FTSE, NIKKEI225, DAX)
- 3.5.3 The case for emerging markets (WIG20, KOSPI, BOVESPA) ...
- 3.6 Summary
- 4.1 Introduction
- 4.2 The merits of investing in volatility
- 4.3.1 Benchmark portfolio
- 4.3.2 Long position in implied volatility
- 4.3.3 Short position in realized volatility
- 4.3.4 A combination of long and short position in volatility
- 4.4 Summary
- 5.1 Introduction
- 5.2 Volatility as a traded asset
- 5.3 Markowitz model – a short review 101
- 5.4 Black-Littermann model – a short review
- 5.5.1 Data used
- 5.5.2 Simulation
- 5.5.3 Empirical results
- 5.6.1 Data used
- 5.6.2 Simulation
- 5.6.3 Empirical results
- 5.7 Summary
- 6.1 Introduction
- 6.2.1 Motivation
- 6.2.2 Literature review
- 6.2.3 Methodology and data
- 6.2.4 Results
- 6.2.5 Remarks
- 6.3.1 Motivation
- 6.3.2 Data description
- 6.3.3 Methodology
- 6.3.4 Measures of volatility term structure
- 6.3.5 Forecasting properties of volatility term structure
- 6.3.6 Investment model
- 6.4 Summary
- Conclusions
- List of figures
- List of tables
- Bibliography

# 1 Volatility and Its Estimation

### Chapter

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## Extract

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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Or login to access all content.- Cover
- Title
- Copyright
- About the author(s)/editor(s)
- About the book
- This eBook can be cited
- Contents
- Introduction
- 1.1 Introduction
- 1.2.1 Alternative volatility estimators
- 1.2.2 High-frequency data
- 1.2.3 Concluding remarks
- 1.3.1 Time series analysis
- 1.3.2 Forecasts implied by option prices
- 1.3.3 Concluding remarks
- 1.4.1 Local volatility model
- 1.4.2 Stochastic volatility models
- 1.4.3 Concluding remarks
- 1.5 Conclusions
- 2.1 Volatility exposure in a delta-hedged option
- 2.2 Variance swaps
- 2.3 VIX and VIX futures
- 2.4 VIX options
- 2.5 The economics of volatility derivatives
- 3.1 Introduction
- 3.2 Options as volatility instruments – replicating realized volatility
- 3.3 Volatility arbitrage based on various frequencies of data
- 3.4 Methodology and data
- 3.5.1 S&P500 index – the most developed market
- 3.5.2 The case for other developed markets (FTSE, NIKKEI225, DAX)
- 3.5.3 The case for emerging markets (WIG20, KOSPI, BOVESPA) ...
- 3.6 Summary
- 4.1 Introduction
- 4.2 The merits of investing in volatility
- 4.3.1 Benchmark portfolio
- 4.3.2 Long position in implied volatility
- 4.3.3 Short position in realized volatility
- 4.3.4 A combination of long and short position in volatility
- 4.4 Summary
- 5.1 Introduction
- 5.2 Volatility as a traded asset
- 5.3 Markowitz model – a short review 101
- 5.4 Black-Littermann model – a short review
- 5.5.1 Data used
- 5.5.2 Simulation
- 5.5.3 Empirical results
- 5.6.1 Data used
- 5.6.2 Simulation
- 5.6.3 Empirical results
- 5.7 Summary
- 6.1 Introduction
- 6.2.1 Motivation
- 6.2.2 Literature review
- 6.2.3 Methodology and data
- 6.2.4 Results
- 6.2.5 Remarks
- 6.3.1 Motivation
- 6.3.2 Data description
- 6.3.3 Methodology
- 6.3.4 Measures of volatility term structure
- 6.3.5 Forecasting properties of volatility term structure
- 6.3.6 Investment model
- 6.4 Summary
- Conclusions
- List of figures
- List of tables
- Bibliography
- Cover
- Title
- Copyright
- About the author(s)/editor(s)
- About the book
- This eBook can be cited
- Contents
- Introduction
- 1.1 Introduction
- 1.2.1 Alternative volatility estimators
- 1.2.2 High-frequency data
- 1.2.3 Concluding remarks
- 1.3.1 Time series analysis
- 1.3.2 Forecasts implied by option prices
- 1.3.3 Concluding remarks
- 1.4.1 Local volatility model
- 1.4.2 Stochastic volatility models
- 1.4.3 Concluding remarks
- 1.5 Conclusions
- 2.1 Volatility exposure in a delta-hedged option
- 2.2 Variance swaps
- 2.3 VIX and VIX futures
- 2.4 VIX options
- 2.5 The economics of volatility derivatives
- 3.1 Introduction
- 3.2 Options as volatility instruments – replicating realized volatility
- 3.3 Volatility arbitrage based on various frequencies of data
- 3.4 Methodology and data
- 3.5.1 S&P500 index – the most developed market
- 3.5.2 The case for other developed markets (FTSE, NIKKEI225, DAX)
- 3.5.3 The case for emerging markets (WIG20, KOSPI, BOVESPA) ...
- 3.6 Summary
- 4.1 Introduction
- 4.2 The merits of investing in volatility
- 4.3.1 Benchmark portfolio
- 4.3.2 Long position in implied volatility
- 4.3.3 Short position in realized volatility
- 4.3.4 A combination of long and short position in volatility
- 4.4 Summary
- 5.1 Introduction
- 5.2 Volatility as a traded asset
- 5.3 Markowitz model – a short review 101
- 5.4 Black-Littermann model – a short review
- 5.5.1 Data used
- 5.5.2 Simulation
- 5.5.3 Empirical results
- 5.6.1 Data used
- 5.6.2 Simulation
- 5.6.3 Empirical results
- 5.7 Summary
- 6.1 Introduction
- 6.2.1 Motivation
- 6.2.2 Literature review
- 6.2.3 Methodology and data
- 6.2.4 Results
- 6.2.5 Remarks
- 6.3.1 Motivation
- 6.3.2 Data description
- 6.3.3 Methodology
- 6.3.4 Measures of volatility term structure
- 6.3.5 Forecasting properties of volatility term structure
- 6.3.6 Investment model
- 6.4 Summary
- Conclusions
- List of figures
- List of tables
- Bibliography