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Dampened Power Law: Reconciling the Tail Behavior of Financial Security Returns

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  • Liuren Wu

    (Zicklin School of Business, Baruch College)

Abstract

This article proposes a stylized model that reconciles several seemingly conflicting findings on financial security returns and option prices. The model is based on a pure jump L�vy process, wherein the jump arrival rate obeys a power law dampened by an exponential function. The model allows for different degrees of dampening for positive and negative jumps and also for different pricing for upside and downside market risks. Calibration of the model to the S&P 500 index shows that the market charges only a moderate premium on upward index movements but the maximally allowable premium on downward index movements.

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Bibliographic Info

Article provided by University of Chicago Press in its journal Journal of Business.

Volume (Year): 79 (2006)
Issue (Month): 3 (May)
Pages: 1445-1474

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Handle: RePEc:ucp:jnlbus:v:79:y:2006:i:3:p:1445-1474

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Cited by:
  1. 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.
  2. Nirei, Makoto & Sushko, Vladyslav, 2011. "Jumps in foreign exchange rates and stochastic unwinding of carry trades," International Review of Economics & Finance, Elsevier, vol. 20(1), pages 110-127, January.
  3. Li, Junye & Favero, Carlo & Ortu, Fulvio, 2012. "A spectral estimation of tempered stable stochastic volatility models and option pricing," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3645-3658.
  4. Zhiguang Wang & Prasad V. Bidarkota, 2008. "A Long-Run Risks Model of Asset Pricing with Fat Tails," Working Papers 0810, Florida International University, Department of Economics.
  5. Dasheng Ji & B. Brorsen, 2011. "A recombining lattice option pricing model that relaxes the assumption of lognormality," Review of Derivatives Research, Springer, vol. 14(3), pages 349-367, October.
  6. Bates, David S., 2012. "U.S. stock market crash risk, 1926–2010," Journal of Financial Economics, Elsevier, vol. 105(2), pages 229-259.
  7. Prasad V. Bidarkota & Brice V. Dupoyet, 2004. "The Impact of Fat Tails on Equilibrium Rates of Return and Term Premia," Working Papers 0411, Florida International University, Department of Economics.
  8. Bidarkota, Prasad V. & Dupoyet, Brice V. & McCulloch, J. Huston, 2009. "Asset pricing with incomplete information and fat tails," Journal of Economic Dynamics and Control, Elsevier, vol. 33(6), pages 1314-1331, June.
  9. Bakshi, Gurdip & Carr, Peter & Wu, Liuren, 2008. "Stochastic risk premiums, stochastic skewness in currency options, and stochastic discount factors in international economies," Journal of Financial Economics, Elsevier, vol. 87(1), pages 132-156, January.
  10. Bakshi, Gurdip & Panayotov, George, 2010. "First-passage probability, jump models, and intra-horizon risk," Journal of Financial Economics, Elsevier, vol. 95(1), pages 20-40, January.
  11. Bates, David S., 2008. "The market for crash risk," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2291-2321, July.

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