Does Historical VIX Term Structure Contain Valuable Information for Predicting VIX Futures?

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

DOI: http://dx.doi.org/10.12775/DEM.2014.001

Abstract


We suggest that the term structure of VIX futures shows a clear pattern of dependence on the current level of VIX index. At the low levels of VIX (below 20), the term structure is highly upward sloping, while at the high VIX levels (over 30) it is strongly downward sloping. We use these features to predict future VIX futures prices more precisely. We begin by introducing some quantitative measures of volatility term structure (VTS) and volatility risk premium (VRP). We use them further to estimate the distance between the actual value and the fair (model) value of the VTS. We find that this distance has significant predictive power for volatility futures and index futures and we use this feature to design simple strategies to invest in VIX futures.

Keywords


volatility term structure; volatility risk premium; VIX, VIX futures; volatility futures; realized volatility; implied volatility; investment strategies; returns forecasting; efficient risk and return measures

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References


Alexander, C., Korovilas D. (2011), The Hazards of Volatility Diversification, ICMA Centre Discussion Papers in Finance DP2011-04, ICMA, DOI: http://dx.doi.org/10.2139/ssrn.1752389.

Andersen, T. G., Bollerslev, T., Christoffersen, P. F., Diebold, F. X. (2005), Volatility Fore-casting, NBER Working Paper 11188, DOI: http://dx.doi.org/10.2139/ssrn.673405.

Asensio, I. O. (2013), The VIX-VIX Futures Puzzle, mimeo.

Bakshi, G., Kapadia, N. (2003), Delta-hedged Gains and the Negative Market Volatility Risk Premium, Review of Financial Studies, 16(2), 527–566.

Black, F., Scholes, M. (1973), The Pricing of Options and Corporate Liabilities, Journal of Political Economy, 81(3), 637–54, DOI: http://dx.doi.org/10.1086/260062.

Bollen, N. P. B., Whaley, R. E. (2004), Does Net Buying Pressure Affect the Shape of Implied Volatility Functions?, Journal of Finance, 59(2), 711–753, DOI: http://dx.doi.org/10.2139/ssrn.319261.

Bondarenko, O. (2004), Market Price of Variance Risk and Performance of Hedge Funds, University of Illinois Chicago working paper.

Bossu, S. (2006), Introduction to Variance Swaps, Wilmott Magazine, 50–55.

Brenner, M., Galai, D. (1989), New Financial Instruments for Hedging Changes in Volatility, Financial Analysts Journal, 45(4), 61–65, DOI: http://dx.doi.org/10.2469/faj.v45.n4.61.

Briere, M., Fermanian, J.-D., Malongo, H., Signori, O. (2011), Volatility Strategies for Global and Country Specific European Investors, DOI: http://dx.doi.org/10.2139/ssrn.1945703.

Carr, P., Lee, R. (2007), Realised Volatility and Variance: Options via Swaps, Risk, 20, 76–83.

Carr, P., Lee, R. (2009), Volatility Derivatives, Annual Review of Financial Economics, 1(1), 319–339, DOI: http://dx.doi.org/10.1146/annurev.financial.050808.114304.

Carr, P., Lewis, K. (2004), Corridor Variance Swaps, Risk, 17, 67–72.

Carr, P., Madan, D. (2001), Towards a Theory of Volatility Trading, [in:] Jarrow, R. (ed.), Volatility. New Estimation Techniques for Pricing Derivatives, in Jouini, E., Cvitanic, J., Musiela, M. (ed.), Option Pricing, Interest Rates and Risk Management, Cambridge University Press, Cambridge, 458–476.

Carr, P., Wu, L. (2009), Variance risk premiums, Review of Financial Studies, 22(3), 1311–1341, DOI: http://dx.doi.org/10.1093/rfs/hhn038.

CBOE (2003), The CBOE Volatility Index – VIX, http://www.cboe.com/micro/vix/vixwhite.pdf.

CBOE (2009), The CBOE Volatility Index – VIX, Chicago Board Options Exchange.

Chen, K., He, X., Poon, S.-H. (2010), The Art of Volatility Modelling. A Case Study Based on DBS, mimeo.

Cox, J. C., Rubinstein, M. (1985), Options Markets. Prentice Hall.

Daigler, R. T., Rossi, L. (2006), A portfolio of stocks and volatility, The Journal of Investing, 15(2), 99–106, DOI: http://dx.doi.org/10.3905/joi.2006.635636.

Dash, S., Moran, M. T. (2005), VIX as a Companion for Hedge Fund Portfolios, The Journal of Alternative Investments, 8(3), 75–80, DOI: http://dx.doi.org/10.3905/jai.2005.608034.

Demeterfi, K., Derman, E., Kamal, M., Zou, J. (1999), A Guide to Volatility and Variance Swaps, The Journal of Derivatives, 6(4), 9–32, DOI: http://dx.doi.org/10.3905/jod.1999.319129.

Derman, E., Demeterfi, K., Kamal, M., Zou, J. (1999), More Than You Ever Wanted To Know About Volatility Swaps, Quantitative strategies research notes, Goldman Sachs.

Derman, E., Kamal, M., Kani, I., McClure, J., Pirasteh, C., Zou, J. Z. (1998), Investing in Volatility, [in:] Futures and Options World, Special Supplement on the 25th Anniver-sary of the Publication of the Black-Scholes Model.

Derman, E., Taleb, N. N. (2005), The Illusions of Dynamic Replication, Quantitative Finance, 5(4), 323–326, DOI: http://dx.doi.org/10.1080/14697680500305105.

Dupire, B. (1993), Model Art, Risk, 6, 118–120.

Dupire, B. (2004), A Unified Theory of Volatility, Working paper, Paribas Capital Markets.

Egloff, D., Leippold, M., Wu, L. (2010), The Term Structure of Variance Swap Rates and Optimal Variance Swap Investments, Journal of Financial and Quantitative Analysis, 45(5), DOI: http://dx.doi.org/10.1017/S0022109010000463.

Fassas, A. P. (2012), The Relationship Between VIX Futures Term Structure and S&P500 Returns, Review of Futures Markets, 20, 293–313.

Fleming, J., Ostdiek, B., Whaley, R. E. (1995), Predicting Stock Market Volatility: A new measure, Journal of Futures Markets, 15(3), 265–302.

Galai, D. (1979), A Proposal for Indexes for Traded Call Options, The Journal of Finance, 34(5), 1157–1172, DOI: http://dx.doi.org/10.2307/2327241.

Gastineau, G. L. (1977), An Index of Listed Option Premiums, Financial Analysts Journal, 33(3), 70–75, DOI: http://dx.doi.org/10.2469/faj.v33.n3.70.

Giot, P. (2005), Relationship between Implied Volatility Index and Stock Index Returns, Journal of Portfolio Management, 31, 92–100.

Guobuzaite, R., Martellini, L. (2012), The Benefits of Volatility Derivatives in Equity Portfolio Management, EDHEC – Risk Institute.

Hafner, R., Wallmeier, M. (2008), Optimal Investments in Volatility, Financial Markets and Portfolio Management, 22(2), 147–167, DOI: http://dx.doi.org/10.1007/s11408-008-0076-8.

Herrmann, R., Luedecke, T. (2002), Why the VOLAX Future Has Failed, [in:] 9thSymposium on Finance, Banking, and Insurance, Universitaet Karlsruhe (TH), Germany.

Huskaj, B., Nossman, M. (2012), A Term Structure Model for VIX Futures, Journal of Fu-tures Markets, 33(5), 421–442, DOI: http://dx.doi.org/10.1002/fut.21550.

Jabłecki, J., Kokoszczyński, R., Sakowski, P., Ślepaczuk, R., Wójcik, P. (2012), Pomiar i modelowanie zmienności – przegląd literatury, Ekonomia, 31, 22–55.

Jabłecki, J., Kokoszczyński, R., Sakowski, P., Ślepaczuk, R., Wójcik, P. (2013a), Struktura czasowa zmienności kontraktów terminowych na VIX – modelowanie i własności pro-gnostyczne, Zarządzanie i Finanse, 11(2), 181–192.

Jabłecki, J., Kokoszczyński, R., Sakowski, P., Ślepaczuk, R., Wójcik, P. (2013b), Instrumenty pochodne na zmienność – nowa klasa aktywów?, WNE UW.

Kitces, M. E. (2012), What Makes Something an Alternative Asset Class, Anyway?, Journal of Financial Planning, 22–23.

Kolanovic, M. (2012), The VIX: Rewards and Risks of a Rapidly Growing Market, Discussion paper, Columbia University Financial Engineering Practitioners Seminar, http://ieor.columbia.edu/financial-engineering-practitioners-seminar.

Konstantinidi, E., Skiadopoulos, G. (2011), Are VIX Futures Prices Predictable? An Empirical Investigation, International Journal of Forecasting, 27, 543–560, DOI: http://dx.doi.org/10.1016/j.ijforecast.2009.11.004.

Merton, R. C. (1973), Theory of Rational Option Pricing, Bell Journal of Economics, 4(1), 141–183, DOI: http://dx.doi.org/10.2307/3003143.

Moran, M. T., Dash, S. (2007), VIX Futures and Options: Pricing and Using Volatility Prod-ucts to Manage Downside Risk and Improve Efficiency in Equity Portfolios, The Journal of Trading, 2(3), 96–105, DOI: http://dx.doi.org/10.3905/jot.2007.688954.

Neuberger, A. (1994), The Log Contract, The Journal of Portfolio Management, 20(2), 74–80, DOI: http://dx.doi.org/10.3905/jpm.1994.409478.

Nieto, B., Novales, A., Rubio, G. (2012), Variance Swaps, Non-normality and Macroeconomic and Financial Risks, The Quarterly Review of Economics and Finance, 54(2), 257–270, DOI: http://dx.doi.org/10.1016/j.qref.2013.12.002.

Signori, O., Briere, M., Burgues, A. (2010), Volatility Exposure for Strategic Asset Allocation, Journal of Portfolio Management, 36(3), 105–116, DOI: http://dx.doi.org/10.3905/jpm.2010.36.3.105.

Simon, D., Wiggins, R. (2001), S&P Futures Returns and Contrary Sentiment Indicators, Journal of Futures Markets, 21, 447–462, DOI: http://dx.doi.org/10.1002/fut.4.

Szado, E. (2009), VIX Futures and Options: A Case Study of Portfolio Diversification during the 2008 Financial Crisis, The Journal of Alternative Investments, 12(2), 68–85.

Whaley, R. E. (1993), Derivatives on Market Volatility: Hedging Tools Long Overdue, Journal of Derivatives, 1, 71–84, DOI: http://dx.doi.org/10.3905/jod.1993.407868.

Yamai, Y., Yoshiba, T. (2005), Value-at-risk versus Expected Shortfall: A Practical Perspec-tive, Journal of Banking & Finance, 29(4), 997–1015, DOI: http://dx.doi.org/10.1016/j.jbankfin.2004.08.010.






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