×

FIX: the fear index – measuring market fear. (English) Zbl 1296.91219

Cummins, Mark (ed.) et al., Topics in numerical methods for finance. Papers based on the presentations at the 3rd international conference, Limerick, Ireland, June 8–10, 2011. New York, NY: Springer (ISBN 978-1-4614-3432-0/hbk; 978-1-4614-3433-7/ebook). Springer Proceedings in Mathematics & Statistics 19, 37-55 (2012).
Summary: In this paper, we propose a new fear index based on (equity) option surfaces of an index and its components. The quantification of the fear level will be solely based on option price data. The index takes into account market risk via the VIX volatility barometer, liquidity risk via the concept of implied liquidity, and systemic risk and herd behavior via the concept of comonotonicity. It thus allows us to measure an overall level of fear (excluding credit risk) in the market as well as to identify precisely the individual importance of the distinct risk components (market, liquidity, or systemic risk). As a an additional result, we also derive an upper bound for the VIX.
For the entire collection see [Zbl 1250.91008].

MSC:

91B82 Statistical methods; economic indices and measures
91G20 Derivative securities (option pricing, hedging, etc.)
91G30 Interest rates, asset pricing, etc. (stochastic models)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Albrecher, H.; Dhaene, J.; Goovaerts, M.; Schoutens, W., Static hedging of Asian options under Lévy models: the comonotonicity approach, J. Derivatives, 12, 3, 63-72 (2005) · doi:10.3905/jod.2005.479381
[2] Albrecher, H., Guillaume, F., Schoutens, W.: Implied liquidity: model dependency investigation. Internal report (2011)
[3] Black, F.; Scholes, M., The pricing of options and corporate liabilities, J. Polit. Econ., 81, 3, 637-654 (1973) · Zbl 1092.91524 · doi:10.1086/260062
[4] Britten-Jones, M.; Neuberger, A., Option prices, implied price processes and stochastic volatility, J Finance, 55, 839-866 (2000) · doi:10.1111/0022-1082.00228
[5] Carr, P., Madan, D.: Towards a theory of volatility trading. In: Jarrow, R. (ed.) Volatility, risk publications, pp. 417—427 (1998)
[6] Carr, P.; Wu, L., A tale of two indices, J. Derivatives, 13, 3, 13-29 (2006) · doi:10.3905/jod.2006.616865
[7] Chen, X.; Deelstra, G.; Dhaene, J.; Vanmaele, M., Static super-replicating strategies for a class of exotic options, Insur. Math. Econ., 42, 3, 1067-1085 (2008) · Zbl 1141.91427 · doi:10.1016/j.insmatheco.2008.01.002
[8] Cherny, A.; Madan, DB, New measures of performance evaluation, Rev. Financ. Stud., 22, 2571-2606 (2009) · doi:10.1093/rfs/hhn081
[9] Cherny, A.; Madan, DB, Markets as a counterparty: an introduction to conic finance, Int. J. Theor. Appl. Finance, 13, 8, 1149-1177 (2010) · Zbl 1208.91148 · doi:10.1142/S0219024910006157
[10] Chicago Board Options Exchange, Inc.: The CBOE volatility index - VIX. White paper (2009)
[11] Corcuera, J.M., Guillaume, F., Madan, D.B., Schoutens, W.: Implied liquidity—towards liquidity modeling and liquidity trading. International Journal of Portfolio Analysis and Management (2012), to appear
[12] Deelstra, G.; Dhaene, J.; Vanmaele, M.; Oksendal, B.; Nunno, G., An overview of comonotonicity and its applications in finance and insurance, Advanced Mathematical Methods for Finance (2010), Germany (Heidelberg): Springer, Germany (Heidelberg)
[13] Demeterfi, K.; Derman, E.; Kamal, M., Zhou (1999), J: More than you ever wanted to know about volatility swaps, Goldman Sachs quantitative strategies research notes, J
[14] Dhaene, J.; Denuit, M.; Goovaerts, M. J.; Kaas, R.; Vyncke, D., The concept of comonotonicity in actuarial science and finance: theory, Insur. Math. Econ. Issue, 1, 31, 3-33 (2002) · Zbl 1051.62107
[15] Dhaene, J., Denuit, M., Goovaerts, M.J., Kaas, R., Vyncke, D.: The concept of comonotonicity in Actuarial science and finance: applications, Insur. Math. Econ. 133-161 (2002) · Zbl 1037.62107
[16] Dhaene, J.; Linders, D.; Schoutens, W.; Vyncke, V., Insurance: Mathematics and economics, 50, 3, 357-370 (2012) · Zbl 1237.91237 · doi:10.1016/j.insmatheco.2012.01.005
[17] Hobson, D.; Laurence, P.; Wang, TH, Static-arbitrage upper bounds for the prices of basket options, Quant. Finance, 5, 4, 329-342 (2005) · Zbl 1134.91425 · doi:10.1080/14697680500151392
[18] Jiang, GJ; Tian, YS, Model-free implied volatility and its information content, Rev. Financ. Stud., 18, 4, 1305-1342 (2005) · doi:10.1093/rfs/hhi027
[19] Laurence, P., Hedging and pricing of generalized spread options and the market implied comonotonicity gap (2007), Vienna University: Presented at the Workshop and Mid-Term Conference on Advanced Mathematical Methods for Finance, Vienna University
[20] Linders, D., Dhaene, J., Schoutens, W.: Some results on comonotonicity based upper bounds for index options. Working paper (2011)
[21] Madan, D.B., Schoutens, W.: Conic financial markets and corporate finance. Int J Theor Appl Finance, 14(5), 587-610 · Zbl 1282.91370
[22] Neuberger, A.: Volatility trading, London Business School working paper (1990)
[23] Simon, S.; Goovaerts, M.; Dhaene, J., An easy computable upper bound for the price of an arithmetic Asian option, Insur. Math. Econ., 26, 2, 175-183 (2001) · Zbl 0964.91021 · doi:10.1016/S0167-6687(99)00051-7
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.