Essays on VIX Futures and Options
(2012) Abstract
 This thesis consists of three essays on VIX futures and options, and deals with issues highly relevant to all financial markets, such as understanding the operation of markets and developing flexible and tractable pricing models for contracts traded in them. It consists of four chapters.
Chapter 1 provides a short introduction to the VIX and a brief explanation of how the old and new VIX are constructed. Thereafter, it discusses VIX derivatives and volatility strategy indexes, and presents other volatility indexes constructed by the Chicago Board Options Exchange. Finally, the chapter provides a short summary of each essay.
Chapter 2 develops a term structure model for VIX futures. Instead of deriving... (More)  This thesis consists of three essays on VIX futures and options, and deals with issues highly relevant to all financial markets, such as understanding the operation of markets and developing flexible and tractable pricing models for contracts traded in them. It consists of four chapters.
Chapter 1 provides a short introduction to the VIX and a brief explanation of how the old and new VIX are constructed. Thereafter, it discusses VIX derivatives and volatility strategy indexes, and presents other volatility indexes constructed by the Chicago Board Options Exchange. Finally, the chapter provides a short summary of each essay.
Chapter 2 develops a term structure model for VIX futures. Instead of deriving the VIX futures price from a model for the instantaneous variance of the S&P 500 or a model for the VIX, the VIX futures price dynamics are specified exogenously. The empirical features of VIX futures returns (positive skewness, excess kurtosis and a decreasing volatility term structure for longer term expirations) are captured by assuming that they are normal inverse Gaussian distributed and scaled by a volatility function that is dependent on the maturity. The usefulness of the resulting model is illustrated in two applications: risk management (via calculating ValueatRisk (VaR)) and asset pricing (via pricing hypothetical VIX options). The results show that the model provides a good fit for the empirical term structure of VIX futures, produces good VaR estimates, and is promising for use in pricing VIX options.
Chapter 3 provides empirical evidence for long memory in the volatility process of VIX futures returns and investigates the practical importance of modelling it when calculating VaR for VIX futures and pricing VIX options. The analysis is performed using the GARCH, APARCH, FIGARCH and FIAPARCH models with the normal and skewed Studentt distributions. The VaR analysis shows that the long memory FIGARCH and FIAPARCH models produce the best outofsample VaR forecasts. The options analysis, however, suggests that the impact of long memory on the pricing of hypothetical VIX options is insignificant.
Chapter 4 investigates the volatilityvolume relation in the VIX futures market. Following [Giot, P., Laurent, S. and Petitjean, M., 2010, Trading activity, realized volatility and jumps, Journal of Empirical Finance, 17, 168175], who examine the relation in the stock market, volatility is measured and decomposed into diffusion and jump components using the modelfree realized volatility estimate. Consistent with the results of Giot et al. (2010), realized continuous (jump) volatility is found to be positively (negatively) related to volume. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/2539860
 author
 Huskaj, Bujar ^{LU}
 supervisor

 Hans Byström ^{LU}
 opponent

 Professor Nordén, Lars, School of Business, Stockholm University
 organization
 publishing date
 2012
 type
 Thesis
 publication status
 published
 subject
 keywords
 NIG, Long memory, Futures, FIGARCH, FIAPARCH, Options, Realized volatility, VaR, VIX, Volume
 pages
 74 pages
 publisher
 Department of Economics, Lund Universtiy
 defense location
 EC3:210, Holger Crafoords Ekonomicentrum, Lund.
 defense date
 20120907 13:15
 ISSN
 04600029
 ISBN
 9789174733389
 language
 English
 LU publication?
 yes
 id
 6b6f474006ae4e43ad0e410068ae8d6c (old id 2539860)
 date added to LUP
 20120522 14:20:06
 date last changed
 20160919 08:44:48
@phdthesis{6b6f474006ae4e43ad0e410068ae8d6c, abstract = {This thesis consists of three essays on VIX futures and options, and deals with issues highly relevant to all financial markets, such as understanding the operation of markets and developing flexible and tractable pricing models for contracts traded in them. It consists of four chapters.<br/><br> <br/><br> Chapter 1 provides a short introduction to the VIX and a brief explanation of how the old and new VIX are constructed. Thereafter, it discusses VIX derivatives and volatility strategy indexes, and presents other volatility indexes constructed by the Chicago Board Options Exchange. Finally, the chapter provides a short summary of each essay.<br/><br> <br/><br> Chapter 2 develops a term structure model for VIX futures. Instead of deriving the VIX futures price from a model for the instantaneous variance of the S&P 500 or a model for the VIX, the VIX futures price dynamics are specified exogenously. The empirical features of VIX futures returns (positive skewness, excess kurtosis and a decreasing volatility term structure for longer term expirations) are captured by assuming that they are normal inverse Gaussian distributed and scaled by a volatility function that is dependent on the maturity. The usefulness of the resulting model is illustrated in two applications: risk management (via calculating ValueatRisk (VaR)) and asset pricing (via pricing hypothetical VIX options). The results show that the model provides a good fit for the empirical term structure of VIX futures, produces good VaR estimates, and is promising for use in pricing VIX options.<br/><br> <br/><br> Chapter 3 provides empirical evidence for long memory in the volatility process of VIX futures returns and investigates the practical importance of modelling it when calculating VaR for VIX futures and pricing VIX options. The analysis is performed using the GARCH, APARCH, FIGARCH and FIAPARCH models with the normal and skewed Studentt distributions. The VaR analysis shows that the long memory FIGARCH and FIAPARCH models produce the best outofsample VaR forecasts. The options analysis, however, suggests that the impact of long memory on the pricing of hypothetical VIX options is insignificant.<br/><br> <br/><br> Chapter 4 investigates the volatilityvolume relation in the VIX futures market. Following [Giot, P., Laurent, S. and Petitjean, M., 2010, Trading activity, realized volatility and jumps, Journal of Empirical Finance, 17, 168175], who examine the relation in the stock market, volatility is measured and decomposed into diffusion and jump components using the modelfree realized volatility estimate. Consistent with the results of Giot et al. (2010), realized continuous (jump) volatility is found to be positively (negatively) related to volume.}, author = {Huskaj, Bujar}, isbn = {9789174733389}, issn = {04600029}, keyword = {NIG,Long memory,Futures,FIGARCH,FIAPARCH,Options,Realized volatility,VaR,VIX,Volume}, language = {eng}, pages = {74}, publisher = {Department of Economics, Lund Universtiy}, school = {Lund University}, title = {Essays on VIX Futures and Options}, year = {2012}, }