Skip to main content
SpringerLink
Log in

Option-Implied Objective Measures of Market Risk with Leverage

  • Conference paper
  • First Online:
Actuarial Sciences and Quantitative Finance (ICASQF 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 214))

Included in the following conference series:

  • 853 Accesses

Abstract

Leverage has been shown to be procyclical and indicative of financial market risk. Here, we present a novel, inherently forward-looking way to estimate market leverage ratios based on derivative prices, option hedging, and the ‘operational’ riskiness measure by Foster and Hart (J Polit Econ 117(5):785–814, 2009). Furthermore, we report option-implied ‘optimal’ leverage levels inferred via the (Kelly, IRE Trans. Inf. Theory 2(3):185–189, 1956) criterion. The resulting measure of leverage exhibits strong procyclicality prior to the Global Financial Crisis of 2008. Finally, we find it to successfully predict large stock market downturns.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The logarithmic growth rate had entered risk analysis already earlier. Examples involve the Kelly (1956) criterion (which aims to maximize growth rate), or, very similar to Foster and Hart (2009), Whitworth (1870, p. 217).

  2. 2.

    Sircar and Papanicolaou (1998) document that dynamic option hedging strategies imply feedback effects between the price of the asset and the price of the derivative, which results in increased volatility.

  3. 3.

    The data is available for purchase at http://www.stricknet.com/. More information on the SPX option contract specifications can be found at http://www.cboe.com/SPX.

  4. 4.

    Our results are robust with respect to choosing a different VaR level.

References

  • Adrian, T., Shin, H.S.: Liquidity and leverage. J. Financ. Intermed. 19(3), 418–437 (2010)

    Article  Google Scholar 

  • Adrian, T., Shin, H.S.: Procyclical leverage and value-at-risk. Rev. Financ. Stud. 27(2), 373–403 (2014)

    Article  Google Scholar 

  • Anand, A., Li, T., Kurosaki, T., Kim, Y.S.: Foster–Hart optimal portfolios. J. Bank. Financ. 68, 117–130 (2016)

    Article  Google Scholar 

  • Aumann, R.J., Serrano, R.: An economic index of riskiness. J. Polit. Econ. 116(5), 810–836 (2008)

    Article  MATH  Google Scholar 

  • Basel Committee on Banking Supervision: Basel III: a global regulatory framework for more resilient banks and banking systems. Technical report, Bank for International Settlements (2010)

    Google Scholar 

  • Black, F., Scholes, M.: The pricing of options and corporate liabilities. J. Polit. Econ. 81(3), 637–654 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  • Breeden, D.T., Litzenberger, R.H.: Prices of state-contingent claims implicit in option prices. J. Bus. 51(4), 621–651 (1978)

    Article  Google Scholar 

  • Chicago Board Options Exchange: The CBOE volatility index – VIX. Technical report, White Paper (2009)

    Google Scholar 

  • Delbaen, F., Schachermayer, W.: A general version of the fundamental theorem of asset pricing. Math. Ann. 300(1), 463–520 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  • Embrechts, P., Klüppelberg, C., Mikosch, T.: Modelling Extremal Events: For Insurance and Finance, vol. 33. Springer, Berlin (1997)

    Book  MATH  Google Scholar 

  • Embrechts, P., Frey, R., McNeil, A.: Quantitative Risk Management, vol. 10. Princeton Series in Finance, Princeton (2005)

    MATH  Google Scholar 

  • Figlewski, S.: Estimating the implied risk neutral density. In: Bollerslev, T., Russell, J., Watson, M. (eds.) Volatility and Time Series Econometrics. Oxford University Press, Oxford (2010)

    Google Scholar 

  • Foster, D.P., Hart, S.: An operational measure of riskiness. J. Polit. Econ. 117(5), 785–814 (2009)

    Article  Google Scholar 

  • Geanakoplos, J.: The leverage cycle. In: NBER Macroeconomics Annual 2009, vol. 24, pp. 1–65. University of Chicago Press, Chicago (2010)

    Google Scholar 

  • Gorton, G., Metrick, A.: Securitized banking and the run on repo. J. Financ. Econ. 104(3), 425–451 (2012)

    Article  Google Scholar 

  • Grossman, S.J., Vila, J.-L.: Optimal dynamic trading with leverage constraints. J. Financ. Quant. Anal. 27(02), 151–168 (1992)

    Article  Google Scholar 

  • Hadar, J., Russell, W.R.: Rules for ordering uncertain prospects. Am. Econ. Rev. 59(1), 25–34 (1969)

    Google Scholar 

  • Hanoch, G., Levy, H.: The efficiency analysis of choices involving risk. Rev. Econ. Stud. 36(3), 335–346 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  • Hildebrand, P.M.: Is Basel II Enough? The Benefits of a Leverage Ratio. Philipp M. Hildebrand, Vice-Chairman of the Governing Board Swiss National Bank, in a Financial Markets Group Lecture at the London School of Economics on December 15, 2008. http://www.ub.unibas.ch/digi/a125/sachdok/2011/BAU_1_5654573.pdf (2008)

  • Jackwerth, J.C.: Option-Implied Risk-Neutral Distributions and Risk Aversion. Research Foundation of AIMR Charlotteville (2004)

    Google Scholar 

  • Kadan, O., Liu, F.: Performance evaluation with high moments and disaster risk. J. Financ. Econ. 113(1), 131–155 (2014)

    Article  Google Scholar 

  • Kelly, J.L.: A new interpretation of information rate. IRE Trans. Inf. Theory 2(3), 185–189 (1956)

    Article  Google Scholar 

  • Leiss, M., Nax, H.H.: Option-implied objective measures of market risk. Social Science Research Network Working Paper Series, 2690476, Quantitative Economics (2015, submitted)

    Google Scholar 

  • Leiss, M., Nax, H.H., Sornette, D.: Super-exponential growth expectations and the global financial crisis. J. Econ. Dyn. Control 55, 1–13 (2015)

    Article  MathSciNet  Google Scholar 

  • Newey, W.K., West, K.D.: A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55(3), 703–708 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  • Newey, W.K., West, K.D.: Automatic lag selection in covariance matrix estimation. Rev. Econ. Stud. 61(4), 631–653 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  • Riedel, F., Hellmann, T.: The Foster-Hart measure of riskiness for general gambles. Theor. Econ. 10(1), 1–9 (2015)

    Article  MATH  MathSciNet  Google Scholar 

  • Rothschild, M., Stiglitz, J.E.: Increasing risk: I. A definition. J. Econ. Theory 2(3), 225–243 (1970)

    Article  MathSciNet  Google Scholar 

  • Schularick, M., Taylor, A.M.: Credit booms gone bust: monetary policy, leverage cycles, and financial crises, 1870–2008. Am. Econ. Rev. 102(2), 1029–1061 (2012)

    Article  Google Scholar 

  • Sharpe, W.F.: The sharpe ratio. J. Portf. Manag. 21(1), 49–58 (1994)

    Article  Google Scholar 

  • Shimko, D.C., Tejima, N., Van Deventer, D.R.: The pricing of risky debt when interest rates are stochastic. J. Fixed Income 3(2), 58–65 (1993)

    Article  Google Scholar 

  • Sircar, R.K., Papanicolaou, G.: General Black-Scholes models accounting for increased market volatility from hedging strategies. Appl. Math. Finance 5(1), 45–82 (1998)

    Article  MATH  Google Scholar 

  • Thurner, S., Farmer, J.D., Geanakoplos, J.: Leverage causes fat tails and clustered volatility. Quant. Finan. 12(5), 695–707 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  • Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B Methodol. 58(1), 267–288 (1996)

    MATH  MathSciNet  Google Scholar 

  • Von der Becke, S., Sornette, D.: Toward a unified framework of credit creation. Technical Report 14-07, Swiss Finance Institute Research Paper (2014)

    Google Scholar 

  • Whitworth, W.: Choice and Chance. Deighton, Bell and Co, Cambridge (1870)

    MATH  Google Scholar 

Download references

Acknowledgements

Leiss acknowledges support from the ETH Risk Center and through SNF grant The Anatomy of Systemic Financial Risk, Nax from the European Commission through the ERC Advanced Investigator Grant Momentum (Grant No. 324247).

Author information

Authors and Affiliations

  1. Department of Humanities, Social and Political Sciences, ETH Zurich, Clausiusstrasse 50, 8092, Zurich, Switzerland

    Matthias Leiss & Heinrich H. Nax

Authors
  1. Matthias Leiss
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Heinrich H. Nax
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Heinrich H. Nax .

Editor information

Editors and Affiliations

  1. Departamento de Matemáticas y Estadí-stica, Universidad Nacional de Colombia, Manizales, Caldas, Colombia

    Jaime A. Londoño

  2. Department of Mathematics and Statistics, Concordia University, Montréal, Québec, Canada

    José Garrido

  3. LaMME, Batiment IBGBI, Université d’Evry Val D’Essone, Evry Cedex, Essonne, France

    Monique Jeanblanc

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Leiss, M., Nax, H.H. (2017). Option-Implied Objective Measures of Market Risk with Leverage. In: Londoño, J., Garrido, J., Jeanblanc, M. (eds) Actuarial Sciences and Quantitative Finance. ICASQF 2016. Springer Proceedings in Mathematics & Statistics, vol 214. Springer, Cham. https://doi.org/10.1007/978-3-319-66536-8_7

Download citation

Publish with us

Policies and ethics

Search

Navigation