# 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:
- 978-3-653-97884-1

- Availability:
- Available

- Subjects:

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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

# 4 Volatility Derivatives in Portfolio Optimization

### Chapter

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## Extract

4.1 Introduction

Over the past decade or so a new class of derivatives has emerged that enable investors to gain direct exposure to volatility. At first glance, the value added of such contracts might seem ambiguous. After all, even plain vanilla options expose investors to volatility as we have already shown. As shown by Black and Scholes (1973) as well as Merton (1973), volatility – i.e. dispersion of the rates of return on a certain underlying instrument – is the key parameter determining the value of an option giving the right to buy (call) or sell (put) that underlying on a certain expiration date. Intuitively, the value of an option to buy a certain stock should be the greater, the greater is the volatility of that stock, since higher volatility means the stock has greater chance of being higher in the money at expiration. The novelty of volatility derivatives, however, is that volatility determines not only the theoretical value of the instrument – as in vanilla options – but also its payoff. Thus, volatility becomes in a sense a new underlying, an asset class in its own right.

This raises three obvious questions. First, how should direct exposure to volatility be understood and why should investors care about obtaining it? Second, assuming some nontrivial advantages of investing in volatility can indeed be identified, how can exposure to volatility be set up in practice? In other words, what are the theoretical underpinnings of the most popular volatility derivatives and...

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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