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Recovering the Real-World Density and Liquidity Premia From Option Data

In this paper we develop a methodology for simultaneous recovery of the real-world probability density and liquidity premia from observed S&P 500 index option prices. Assuming the existence of a num´eraire portfolio for the US equity market, fair prices of derivatives under the benchmark approach can be obtained directly under the real-world measure. Under this modeling framework there exists a direct link between observed call option prices on the index and the real-world density for the underlying index. We use a novel method for estimation of option implied volatility surfaces of high quality, which enables the subsequent analysis. We show that the real-world density that we recover is consistent with the observed realized dynamics of the underlying index. This admits the identification of liquidity premia embedded in option price data. We identify and estimate two separate liquidity premia embedded in S&P 500 index options that are consistent with previous findings in the literature.

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File URL: https://www.uts.edu.au/sites/default/files/qfr-archive-03/QFR-rp363.pdf
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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 363.

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Length: 32 pages
Date of creation: 01 Sep 2015
Publication status: Published as: Barkhagen, M., Blomvall, J. and Platen, E., 2016, "Recovering the Real-World Density and Liquidity Premia From Option Data", Quantitative Finance, 16(7), 1147-1164.
Handle: RePEc:uts:rpaper:363
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  1. Kristensen, Dennis & Shin, Yongseok, 2012. "Estimation of dynamic models with nonparametric simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 167(1), pages 76-94.
  2. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
  3. David Heath & Eckhard Platen, 2006. "Local volatility function models under a benchmark approach," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 197-206.
  4. Steve Ross, 2015. "The Recovery Theorem," Journal of Finance, American Finance Association, vol. 70(2), pages 615-648, April.
  5. Baldeaux, Jan & Grasselli, Martino & Platen, Eckhard, 2015. "Pricing currency derivatives under the benchmark approach," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 34-48.
  6. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 1-22, March.
  7. Renata Rendek, 2013. "Modeling Diversified Equity Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 23, December.
  8. Eckhard Platen & Renata Rendek, 2012. "The Affine Nature of Aggregate Wealth Dynamics," Research Paper Series 322, Quantitative Finance Research Centre, University of Technology, Sydney.
  9. 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, April.
  10. Bera, Anil K. & Jarque, Carlos M., 1981. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals : Monte Carlo Evidence," Economics Letters, Elsevier, vol. 7(4), pages 313-318.
  11. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
  12. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
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