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Option Prices in a Model with Stochastic Disaster Risk

Author

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  • Sang Byung Seo

    (University of Houston, Houston, Texas 77204)

  • Jessica A. Wachter

    (University of Pennsylvania, Philadelphia, Pennsylvania 19104; and National Bureau of Economic Research, Cambridge, Massachusetts 02138)

Abstract

Contrary to well-known asset pricing models, volatilities implied by equity index options exceed realized stock market volatility and exhibit a pattern known as the volatility skew. We explain both facts using a model that can also account for the mean and volatility of equity returns. Our model assumes a small risk of economic disaster that is calibrated based on international data on large consumption declines. We allow the disaster probability to be stochastic, which turns out to be crucial to the model’s ability both to match equity volatility and to reconcile option prices with macroeconomic data on disasters.

Suggested Citation

  • Sang Byung Seo & Jessica A. Wachter, 2019. "Option Prices in a Model with Stochastic Disaster Risk," Management Science, INFORMS, vol. 65(8), pages 3449-3469, August.
    • Handle: RePEc:inm:ormnsc:v:65:y:2019:i:8:p:3449-3469
    DOI: 10.1287/mnsc.2017.2978
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    as
    1. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    2. David Backus & Mikhail Chernov & Ian Martin, 2011. "Disasters Implied by Equity Index Options," Journal of Finance, American Finance Association, vol. 66(6), pages 1969-2012, December.
    3. Erik Vogt, 2014. "Option-implied term structures," Staff Reports 706, Federal Reserve Bank of New York.
    4. George Chacko & Luis M. Viceira, 2005. "Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets," Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1369-1402.
    5. Robert J. Barro & Tao Jin, 2011. "On the Size Distribution of Macroeconomic Disasters," Econometrica, Econometric Society, vol. 79(5), pages 1567-1589, September.
    6. Tim Bollerslev & George Tauchen & Hao Zhou, 2009. "Expected Stock Returns and Variance Risk Premia," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4463-4492, November.
    7. Bryan Kelly & Ľuboš Pástor & Pietro Veronesi, 2016. "The Price of Political Uncertainty: Theory and Evidence from the Option Market," Journal of Finance, American Finance Association, vol. 71(5), pages 2417-2480, October.
    8. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
    9. Bates, David S., 2008. "The market for crash risk," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2291-2321, July.
    10. David Backus & Mikhail Chernov & Stanley Zin, 2014. "Sources of Entropy in Representative Agent Models," Journal of Finance, American Finance Association, vol. 69(1), pages 51-99, February.
    11. Jerry Tsai & Jessica A. Wachter, 2015. "Disaster Risk and its Implications for Asset Pricing," NBER Working Papers 20926, National Bureau of Economic Research, Inc.
    12. Philippe Weil, 1990. "Nonexpected Utility in Macroeconomics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 105(1), pages 29-42.
    13. Dew-Becker, Ian & Giglio, Stefano & Le, Anh & Rodriguez, Marius, 2017. "The price of variance risk," Journal of Financial Economics, Elsevier, vol. 123(2), pages 225-250.
    14. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
    15. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    16. Tim Bollerslev & Viktor Todorov, 2011. "Tails, Fears, and Risk Premia," Journal of Finance, American Finance Association, vol. 66(6), pages 2165-2211, December.
    17. John Y. Campbell & John Cochrane, 1999. "Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," Journal of Political Economy, University of Chicago Press, vol. 107(2), pages 205-251, April.
    18. John Y. Campbell, Robert J. Shiller, 1988. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 195-228.
    19. Pedro Santa-Clara & Shu Yan, 2010. "Crashes, Volatility, and the Equity Premium: Lessons from S&P 500 Options," The Review of Economics and Statistics, MIT Press, vol. 92(2), pages 435-451, May.
    20. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    21. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    22. Jessica A. Wachter, 2013. "Can Time-Varying Risk of Rare Disasters Explain Aggregate Stock Market Volatility?," Journal of Finance, American Finance Association, vol. 68(3), pages 987-1035, June.
    23. George M. Constantinides & Jens Carsten Jackwerth & Stylianos Perrakis, 2009. "Mispricing of S&P 500 Index Options," The Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 1247-1277, March.
    24. Martin Lettau & Sydney C. Ludvigson & Jessica A. Wachter, 2008. "The Declining Equity Premium: What Role Does Macroeconomic Risk Play?," Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1653-1687, July.
    25. Jerry Tsai & Jessica A. Wachter, 2015. "Disaster Risk and Its Implications for Asset Pricing," Annual Review of Financial Economics, Annual Reviews, vol. 7(1), pages 219-252, December.
    26. Emi Nakamura & Jón Steinsson & Robert Barro & José Ursúa, 2013. "Crises and Recoveries in an Empirical Model of Consumption Disasters," American Economic Journal: Macroeconomics, American Economic Association, vol. 5(3), pages 35-74, July.
    27. Christoffersen, Peter & Jacobs, Kris, 2004. "The importance of the loss function in option valuation," Journal of Financial Economics, Elsevier, vol. 72(2), pages 291-318, May.
    28. Shiller, Robert J, 1981. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," American Economic Review, American Economic Association, vol. 71(3), pages 421-436, June.
    29. Jerry Tsai, 2013. "Rare Disasters and the Term Structure of Interest Rates," Economics Series Working Papers 665, University of Oxford, Department of Economics.
    30. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    31. Yan, Shu, 2011. "Jump risk, stock returns, and slope of implied volatility smile," Journal of Financial Economics, Elsevier, vol. 99(1), pages 216-233, January.
    32. G.M. Constantinides & M. Harris & R. M. Stulz (ed.), 2003. "Handbook of the Economics of Finance," Handbook of the Economics of Finance, Elsevier, edition 1, volume 1, number 1.
    33. Shaliastovich, Ivan, 2015. "Learning, confidence, and option prices," Journal of Econometrics, Elsevier, vol. 187(1), pages 18-42.
    34. Xavier Gabaix, 2012. "Variable Rare Disasters: An Exactly Solved Framework for Ten Puzzles in Macro-Finance," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(2), pages 645-700.
    35. Manela, Asaf & Moreira, Alan, 2017. "News implied volatility and disaster concerns," Journal of Financial Economics, Elsevier, vol. 123(1), pages 137-162.
    36. Benzoni, Luca & Collin-Dufresne, Pierre & Goldstein, Robert S., 2011. "Explaining asset pricing puzzles associated with the 1987 market crash," Journal of Financial Economics, Elsevier, vol. 101(3), pages 552-573, September.
    37. Barro, Robert J. & Ursúa, José F., 2017. "Stock-market crashes and depressions," Research in Economics, Elsevier, vol. 71(3), pages 384-398.
    38. Du, Du, 2011. "General equilibrium pricing of options with habit formation and event risks," Journal of Financial Economics, Elsevier, vol. 99(2), pages 400-426, February.
    39. Berkman, Henk & Jacobsen, Ben & Lee, John B., 2011. "Time-varying rare disaster risk and stock returns," Journal of Financial Economics, Elsevier, vol. 101(2), pages 313-332, August.
    40. Robert J. Barro, 2006. "Rare Disasters and Asset Markets in the Twentieth Century," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(3), pages 823-866.
    41. Joshua D. Coval & Tyler Shumway, 2001. "Expected Option Returns," Journal of Finance, American Finance Association, vol. 56(3), pages 983-1009, June.
    42. Breeden, Douglas T., 1979. "An intertemporal asset pricing model with stochastic consumption and investment opportunities," Journal of Financial Economics, Elsevier, vol. 7(3), pages 265-296, September.
    43. Jun Liu, 2005. "An Equilibrium Model of Rare-Event Premia and Its Implication for Option Smirks," Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 131-164.
    44. Longstaff, Francis A. & Piazzesi, Monika, 2004. "Corporate earnings and the equity premium," Journal of Financial Economics, Elsevier, vol. 74(3), pages 401-421, December.
    45. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    46. Lior Menzly & Tano Santos & Pietro Veronesi, 2004. "Understanding Predictability," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 1-47, February.
    47. Graham, John R. & Leary, Mark T. & Roberts, Michael R., 2015. "A century of capital structure: The leveraging of corporate America," Journal of Financial Economics, Elsevier, vol. 118(3), pages 658-683.
    48. Philippe Jorion & William N. Goetzmann, 1999. "Global Stock Markets in the Twentieth Century," Journal of Finance, American Finance Association, vol. 54(3), pages 953-980, June.
    49. Ravi Bansal & Amir Yaron, 2004. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, August.
    50. Bjørn Eraker, 2004. "Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices," Journal of Finance, American Finance Association, vol. 59(3), pages 1367-1404, June.
    51. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    52. Andrea Buraschi & Alexei Jiltsov, 2006. "Model Uncertainty and Option Markets with Heterogeneous Beliefs," Journal of Finance, American Finance Association, vol. 61(6), pages 2841-2897, December.
    53. George Tauchen, 2011. "Stochastic Volatility in General Equilibrium," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 1(04), pages 707-731.
    54. Campbell, John Y., 2003. "Consumption-based asset pricing," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 13, pages 803-887, Elsevier.
    55. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    56. Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1998. "Implied Volatility Functions: Empirical Tests," Journal of Finance, American Finance Association, vol. 53(6), pages 2059-2106, December.
    57. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    58. Peter Carr & Liuren Wu, 2009. "Variance Risk Premiums," Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 1311-1341, March.
    59. Sang Byung Seo & Jessica A. Wachter, 2018. "Do Rare Events Explain CDX Tranche Spreads?," Journal of Finance, American Finance Association, vol. 73(5), pages 2343-2383, October.
    60. Itamar Drechsler, 2013. "Uncertainty, Time-Varying Fear, and Asset Prices," Journal of Finance, American Finance Association, vol. 68(5), pages 1843-1889, October.
    61. Robert J. Barro & Jose F. Ursua, 2008. "Macroeconomic Crises since 1870," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 39(1 (Spring), pages 255-350.
    62. Naik, Vasanttilak & Lee, Moon, 1990. "General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 493-521.
    63. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    64. Mark Broadie & Mikhail Chernov & Michael Johannes, 2007. "Model Specification and Risk Premia: Evidence from Futures Options," Journal of Finance, American Finance Association, vol. 62(3), pages 1453-1490, June.
    65. Abel, Andrew B., 1999. "Risk premia and term premia in general equilibrium," Journal of Monetary Economics, Elsevier, vol. 43(1), pages 3-33, February.
    66. G.M. Constantinides & M. Harris & R. M. Stulz (ed.), 2003. "Handbook of the Economics of Finance," Handbook of the Economics of Finance, Elsevier, edition 1, volume 1, number 2.
    67. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
    68. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
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