Can Standard Preferences Explain the Prices of out of the Money S&P 500 Put Options
Prior to the stock market crash of 1987, Black-Scholes implied volatilities of S&P 500 index options were relatively constant across moneyness. Since the crash, however, deep out-of-the-money S&P 500 put options have become %u2018expensive%u2019 relative to the Black-Scholes benchmark. Many researchers (e.g., Liu, Pan and Wang (2005)) have argued that such prices cannot be justified in a general equilibrium setting if the representative agent has %u2018standard preferences%u2019 and the endowment is an i.i.d. process. Below, however, we use the insight of Bansal and Yaron (2004) to demonstrate that the %u2018volatility smirk%u2019 can be rationalized if the agent is endowed with Epstein-Zin preferences and if the aggregate dividend and consumption processes are driven by a persistent stochastic growth variable that can jump. We identify a realistic calibration of the model that simultaneously matches the empirical properties of dividends, the equity premium, the prices of both at-the-money and deep out-of-the-money puts, and the level of the risk-free rate. A more challenging question (that to our knowledge has not been previously investigated) is whether one can explain within a standard preference framework the stark regime change in the volatility smirk that has maintained since the 1987 market crash. To this end, we extend the model to a Bayesian setting in which the agent updates her beliefs about the average jump size in the event of a jump. Note that such beliefs only update at crash dates, and hence can explain why the volatility smirk has not diminished over the last eighteen years. We find that the model can capture the shape of the implied volatility curve both pre- and post-crash while maintaining reasonable estimates for expected returns, price-dividend ratios, and risk-free rates.
|Date of creation:||Dec 2005|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://www.nber.org
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 2000.
"Pricing and hedging long-term options,"
Journal of Econometrics,
Elsevier, vol. 94(1-2), pages 277-318.
- Chacko, George & Viceira, Luis M., 2003. "Spectral GMM estimation of continuous-time processes," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 259-292.
- David S. Bates, 2001. "The Market for Crash Risk," NBER Working Papers 8557, National Bureau of Economic Research, Inc.
- Mikhail Chernov & A. Ronald Gallant & Eric Ghysels & George Tauchen, 2002.
"Alternative Models for Stock Price Dynamics,"
CIRANO Working Papers
- Mikhail Chernov & A. Ronald Gallant & Eric Ghysels & George Tauchen, 1999. "A New Class of Stochastic Volatility Models with Jumps: Theory and Estimation," CIRANO Working Papers 99s-48, CIRANO.
- Gurdip Bakshi & Nikunj Kapadia, 2003. "Delta-Hedged Gains and the Negative Market Volatility Risk Premium," Review of Financial Studies, Society for Financial Studies, vol. 16(2), pages 527-566.
- Long Chen & Pierre Collin-Dufresne & Robert S. Goldstein, 2009. "On the Relation Between the Credit Spread Puzzle and the Equity Premium Puzzle," Review of Financial Studies, Society for Financial Studies, vol. 22(9), pages 3367-3409, September.
- Andrew B. Abel, 1998.
"Risk Premia and Term Premia in General Equilibrium,"
NBER Working Papers
6683, National Bureau of Economic Research, Inc.
- Abel, Andrew B., 1999. "Risk premia and term premia in general equilibrium," Journal of Monetary Economics, Elsevier, vol. 43(1), pages 3-33, February.
- Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
- John Y. Campbell & Robert J. Shiller, 1986.
"The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors,"
NBER Working Papers
2100, National Bureau of Economic Research, Inc.
- 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.
- Robert J. Shiller & John Y. Campbell, 1986. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," Cowles Foundation Discussion Papers 812, Cowles Foundation for Research in Economics, Yale University.
- Bansal, Ravi & Lundblad, Christian, 2002. "Market efficiency, asset returns, and the size of the risk premium in global equity markets," Journal of Econometrics, Elsevier, vol. 109(2), pages 195-237, August.
- Nicolas P. B. Bollen & Robert E. Whaley, 2004. "Does Net Buying Pressure Affect the Shape of Implied Volatility Functions?," Journal of Finance, American Finance Association, vol. 59(2), pages 711-753, 04.
- Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
- 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, 08.
- Ravi Bansal & Amir Yaron, 2000. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," NBER Working Papers 8059, National Bureau of Economic Research, Inc.
- Robert J. Barro, 2005. "Rare Events and the Equity Premium," NBER Working Papers 11310, National Bureau of Economic Research, Inc.
- Buraschi, Andrea & Jackwerth, Jens, 2001. "The Price of a Smile: Hedging and Spanning in Option Markets," Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 495-527.
- Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
- Attanasio, Orazio P & Weber, Guglielmo, 1989. "Intertemporal Substitution, Risk Aversion and the Euler Equation for Consumption," Economic Journal, Royal Economic Society, vol. 99(395), pages 59-73, Supplemen.
When requesting a correction, please mention this item's handle: RePEc:nbr:nberwo:11861. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
If references are entirely missing, you can add them using this form.