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Options-Pricing Formula with Disaster Risk

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  • Robert J. Barro
  • Gordon Y. Liao

Abstract

A new options-pricing formula applies to far-out-of-the money put options on the overall stock market when disaster risk is the dominant force, the size distribution of disasters follows a power law, and the economy has a representative agent with Epstein-Zin utility. In the applicable region, the elasticity of the put-options price with respect to maturity is close to one. The elasticity with respect to exercise price is greater than one, roughly constant, and depends on the difference between the power-law tail parameter and the coefficient of relative risk aversion, γ. The options-pricing formula conforms with data from 1983 to 2015 on far-out-of-the-money put options on the U.S. S&P 500 and analogous indices for other countries. The analysis uses two types of data—indicative prices on OTC contracts offered by a large financial firm and market data provided by OptionMetrics, Bloomberg, and Berkeley Options Data Base. The options-pricing formula involves a multiplicative term that is proportional to the disaster probability, p. If γ and the size distribution of disasters are fixed, time variations in p can be inferred from time fixed effects. The estimated disaster probability peaks particularly during the recent financial crisis of 2008-09 and the stock-market crash of October 1987.

Suggested Citation

  • Robert J. Barro & Gordon Y. Liao, 2016. "Options-Pricing Formula with Disaster Risk," NBER Working Papers 21888, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:21888
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    Cited by:

    1. Horvath, Jaroslav, 2019. "Isolating the disaster risk premium with equity options," Journal of Empirical Finance, Elsevier, vol. 51(C), pages 138-148.
    2. Gabriel Chodorow-Reich & Loukas Karabarbounis & Rohan Kekre, 2023. "The Macroeconomics of the Greek Depression," American Economic Review, American Economic Association, vol. 113(9), pages 2411-2457, September.
    3. Robert Barro & Tao Jin, 2021. "Rare Events and Long-Run Risks," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 39, pages 1-25, January.
    4. Natasha Sarin & Lawrence H. Summers, 2016. "Understanding Bank Risk through Market Measures," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 47(2 (Fall)), pages 57-127.
    5. Gourieroux, Christian & Jasiak, Joann, 2010. "Inference for Noisy Long Run Component Process," MPRA Paper 98987, University Library of Munich, Germany.
    6. Zhiguo He & Arvind Krishnamurthy, 2018. "Intermediary Asset Pricing and the Financial Crisis," Annual Review of Financial Economics, Annual Reviews, vol. 10(1), pages 173-197, November.
    7. Bruno Ćorić & Vladimir Šimić, 2021. "Economic disasters and aggregate investment," Empirical Economics, Springer, vol. 61(6), pages 3087-3124, December.
    8. Ian Martin, 2017. "What is the Expected Return on the Market?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(1), pages 367-433.
    9. Christian Gouriéroux & Alain Monfort & Sarah Mouabbi & Jean-Paul Renne, 2021. "Disastrous Defaults [Risk premia and term premia in general equilibrium]," Review of Finance, European Finance Association, vol. 25(6), pages 1727-1772.
    10. repec:oup:qjecon:v:132:y:2016:i:1:p:367-433. is not listed on IDEAS
    11. Natasha Sarin & Lawrence H. Summers, 2016. "Understanding Bank Risk through Market Measures," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 47(2 (Fall)), pages 57-127.
    12. Robert Barro & Tao Jin, 2021. "Rare Events and Long-Run Risks," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 39, pages 1-25, January.

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    More about this item

    JEL classification:

    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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