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On valuing and hedging European options when volatility is estimated directly

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  • Popovic, Ray
  • Goldsman, David

Abstract

We quantify the effects on contingent claim valuation of using an estimator for the unknown volatility σ of a geometric Brownian motion (GBM) process. The theme of the paper is to show what difficulties can arise when failing to account for estimation risk. Our narrative uses a direct estimator of volatility based on the sample standard deviation of increments of the underlying Brownian motion. After replacing the direct estimator into the GBM, we derive the resulting distribution function of the approximated GBM for any time point. This allows us to present post-estimation distributions and valuation formulae for an assortment of European contingent claims that are in accord with many of the basic properties of the underlying risk-neutral process, and yet better reflect the additional uncertainties and risks that exist in the Black–Scholes–Merton paradigm.

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  • Popovic, Ray & Goldsman, David, 2012. "On valuing and hedging European options when volatility is estimated directly," European Journal of Operational Research, Elsevier, vol. 218(1), pages 124-131.
    • Handle: RePEc:eee:ejores:v:218:y:2012:i:1:p:124-131
    DOI: 10.1016/j.ejor.2011.09.011
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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Castellacci, Giuseppe & Siclari, Michael J., 2003. "The practice of Delta-Gamma VaR: Implementing the quadratic portfolio model," European Journal of Operational Research, Elsevier, vol. 150(3), pages 529-545, November.
    3. Cifarelli, Michele D. & Masciandaro, Donato & Peccati, Lorenzo & Salsa, Sandro & Tagliani, Aldo, 2002. "Success or failure of a firm under different financing policies: A dynamic stochastic model," European Journal of Operational Research, Elsevier, vol. 136(3), pages 471-482, February.
    4. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2008. "A dynamic stochastic programming model for international portfolio management," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1501-1524, March.
    5. 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.
    6. Boyle, Phelim P. & Ananthanarayanan, A. L., 1977. "The impact of variance estimation in option valuation models," Journal of Financial Economics, Elsevier, vol. 5(3), pages 375-387, December.
    7. Lucas, Robert Jr, 1976. "Econometric policy evaluation: A critique," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 1(1), pages 19-46, January.
    8. Butler, J. S. & Schachter, Barry, 1986. "Unbiased estimation of the Black/Scholes formula," Journal of Financial Economics, Elsevier, vol. 15(3), pages 341-357, March.
    9. Mthuli Ncube & Stephen Satchell, 1997. "The Statistical Properties of the Black–Scholes Option Price," Mathematical Finance, Wiley Blackwell, vol. 7(3), pages 287-305, July.
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    2. Marcos Escobar & Sven Panz, 2016. "A Note on the Impact of Parameter Uncertainty on Barrier Derivatives," Risks, MDPI, vol. 4(4), pages 1-25, September.

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