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Rev Quant Finan Acc (2010) 35:245269
DOI 10.1007/s11156-009-0153-8
ORIGINAL RESEARCH
Dimitris Psychoyios George Dotsis Raphael N. Markellos
Published online: 11 December 2009 Springer Science+Business Media, LLC 2009
Abstract Volatility indices are becoming increasingly popular as a measure of market uncertainty and as a new asset class for developing derivative instruments. Although jumps are widely considered as a salient feature of volatility, their implications for pricing volatility options and futures are not yet fully understood. This paper provides evidence indicating that the time series behaviour of the VIX index is well approximated by a mean reverting logarithmic diffusion with jumps. This process is capable of capturing stylized facts of VIX dynamics such as fast mean-reversion at higher levels, level effects of volatility and large upward movements during times of market stress. Based on the empirical results, we provide closed-form valuation models for European options written on the spot and forward VIX, respectively.
D. Psychoyios
Department of Industrial Management, University of Piraeus, Deligiorgi 107, 185 34 Piraeus, Greecee-mail: [email protected]
D. Psychoyios
CAIR, Manchester Business School, University of Manchester, Booth Street East, Manchester M13 9PL, UK
G. Dotsis (&)
Essex Business School and Essex Finance Centre,University of Essex, Wivenhoe Park, Colchester C04 3SQ, UK e-mail: [email protected]
R. N. Markellos
Department of Management Science and Technology, Athens University of Economics and Business, Ofce 915, 47A Evelpidon Str., 113 62 Athens, Greecee-mail: [email protected]
R. N. Markellos
Centre for Research in International Economics and Finance (CIFER), Loughborough University, Loughborough, UK
A jump diffusion model for VIX volatility options and futures
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Keywords Implied volatility Jump diffusion Option pricing Volatility risk
JEL Classication G13 C51 C52
1 Introduction
Volatility is undoubtedly one of the most important variables in nance, appearing in a wide spectrum of theories and applications in asset pricing, portfolio theory, risk management, derivatives, corporate nance, investment evaluation and econometrics. A fascinating recent development has been the treatment of volatility as a distinct asset which can be packaged in an index and traded using futures and options (hereinafter collectively referred to as volatility derivatives).1 Volatility derivatives provide new ways to trade and hedge volatility risk and are considered by some to have the potential to be one of the most important new nancial innovations (Grnbichler...