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The cross-section of average delta-hedge option returns under stochastic volatility

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Abstract

Existing evidence indicates that average returns of purchased market-hedge S&P 500 index calls, puts, and straddles are non-zero but large and negative, which implies that options are expensive. This result is intuitively explained by means of volatility risk and a negative volatility risk premium, but there is a recent surge of empirical and analytical studies which also attempt to find the sources of this premium. An important question in the line of a priced volatility explanation is if a standard stochastic volatility model can also explain the cross-sectional findings of these empirical studies. The answer is fairly positive. The volatility elasticity of calls and puts is several times the level of market volatility, depending on moneyness and maturity, and implies a rich cross-section of negative average option returns—even if volatility risk is not priced heavily, albeit negative. We introduce and calibrate a new measure of option overprice to explain these results. This measure is robust to jump risk if jumps are not priced.

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References

  • Aït-Sahalia Y., Wang Y., Yared F. (2001) Do option markets correctly price the probabilities of movement of the Underlying Asset?. Journal of Econometrics 102: 67–110

    Article  Google Scholar 

  • Bakshi G., Kapadia N. (2003a) Delta-hedged gains and the negative market volatility risk premium. Review of Financial Studies 16: 527–566

    Article  Google Scholar 

  • Bakshi G., Kapadia N. (2003b) Volatility risk premium embedded in individual equity options: Some new insights. Journal of Derivatives 11: 45–54

    Google Scholar 

  • Bates D. (1996) Jumps and stochastic volatility: Exchange rates processes implicit in deutsche mark options. Review of Financial Studies 9: 69–107

    Article  Google Scholar 

  • Benzoni, L., Collin-Dufresne, P., & Goldstein, R. (2005). Can standard preferences explain the prices of out-of-the-money puts. University of Minnesota, Working Paper.

  • Bondarenko, O. (2003). Why are puts so expensive. University of Illinois at Chicago, Working Paper.

  • Branger N., Schlag C. (2008) Can tests based on option hedging errors correctly identify volatility risk premia?. Journal of Financial and Quantitative Analysis 43: 1055–1090

    Article  Google Scholar 

  • Broadie, M., Chernov, M., & Johannes, M. (2009). Understanding index option returns. Review of Financial Studies (forthcoming).

  • Buraschi A., Jackwerth J. (2001) The price of a smile: Hedging and spanning in option markets. Review of Financial Studies 14: 495–527

    Article  Google Scholar 

  • Cao C., Huang J.-Z. (2008) Determinants of S&P 500 index option returns. Review of Derivatives Research 10: 1–38

    Article  Google Scholar 

  • Carr P., Wu L. (2003) What type of process underlies options? A simple robust test. Journal of Finance 58: 2581–2610

    Article  Google Scholar 

  • Carr P., Wu L. (2006) A tale of two indices. Journal of Derivatives 13(3): 13–29

    Google Scholar 

  • Carr P., Wu L. (2009) Variance risk premia. Review of Financial Studies 22: 1311–1341

    Article  Google Scholar 

  • Constantinides G.M., Jackwerth J.C., Perrakis S. (2009) Mispricing of S&P 500 index options. Review of Financial Studies 22: 1247–1277

    Article  Google Scholar 

  • Coval J., Shumway T. (2001) Expected option returns. Journal of Finance 56: 983–1009

    Article  Google Scholar 

  • Christoffersen, P. F., Heston, S. L., & Jacobs, K. (2007). The Shape and term structure of the index option smirk: Why multifactor stochastic volatility models work so well. University of Maryland, Working Paper.

  • Driessen, J., Maenhout, P., & Vilkov, G. (2009). The price of correlation risk: Evidence from equity options. Journal of Finance (forthcoming).

  • Duffee G. (2002) Term premia and interest rate forecasts in affine models. Journal of Finance 57: 405–443

    Article  Google Scholar 

  • Duffie D. (2001) Dynamic asset pricing theory (3rd ed). Princeton University Press, Princeton, New Jersey

    Google Scholar 

  • Duffie D., Pan J., Singleton K. (2000) Transform analysis and asset pricing for affine jump-diffusions. Econometrica 68: 1343–1376

    Article  Google Scholar 

  • Eraker B., Johannes M., Polson N. (2003) The impact of jumps in volatility and returns. Journal of Finance 58: 1269–1300

    Article  Google Scholar 

  • Figlewski S., Green T.C. (1999) Market risk and model risk for a financial institution writing options. Journal of Finance 54: 1465–1499

    Article  Google Scholar 

  • Garleanu, N., Pedersen, L. H., & Poteshman, A. (2009). Demand-based option pricing. Review of Financial Studies (forthcoming).

  • Heston S. (1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies 6: 327–344

    Article  Google Scholar 

  • Ibáñez A. (2008) Factorization of European and American option prices under complete and incomplete markets. Journal of Banking and Finance 32: 311–325

    Article  Google Scholar 

  • Jiang G.J., Tian Y.S. (2005) The model-free implied volatility and its information content. Review of Financial Studies 18: 1305–1342

    Article  Google Scholar 

  • Jones C. (2006) A nonlinear factor analysis of S&P 500 index options returns. Journal of Finance 41: 2325–2363

    Article  Google Scholar 

  • Liu J., Pan J. (2003) Dynamic derivative strategies. Journal of Financial Economics 69: 401–430

    Article  Google Scholar 

  • Low B.S., Zhang S. (2005) The volatility risk premium embedded in currency options. Journal of Financial and Quantitative Analysis 40: 803–832

    Google Scholar 

  • Merton R. (1998) Applications of option-pricing theory: Twenty-five years later. The Nobel prize in economics lecture. American Economic Review 88: 323–349

    Google Scholar 

  • Naik V., Lee M. (1990) General equilibrium pricing of options on the market portfolio with discontinuous returns. Review of Financial Studies 3: 493–521

    Article  Google Scholar 

  • Nandi S. (1998) How important is the correlation between returns and volatility in a stochastic volatility model? Empirical evidence from pricing and hedging in the S&P 500 index options market. Journal of Banking and Finance 22: 589–610

    Article  Google Scholar 

  • Pan J. (2002) The jump-risk premia implicit in options: Evidenced from an integrated time-series study. Journal of Financial Economics 63: 3–50

    Article  Google Scholar 

  • Santa-Clara, P., & Saretto, A. (2009). Option strategies: Good deals and margin calls. Journal of Financial Markets (forthcoming).

  • Wu, L. (2007). Variance dynamics: Joint evidence from options and high-frequency returns. Baruch College, Working Paper.

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  1. Quantitative Development, Treasury, Caja Madrid, Po de la Castellana, 189, 3a planta, 28046, Madrid, Spain

    Alfredo Ibáñez

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  1. Alfredo Ibáñez
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Correspondence to Alfredo Ibáñez.

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Ibáñez, A. The cross-section of average delta-hedge option returns under stochastic volatility. Rev Deriv Res 11, 205–244 (2008). https://doi.org/10.1007/s11147-009-9030-9

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  • DOI: https://doi.org/10.1007/s11147-009-9030-9

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