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Symmetry and Bates’ rule in Ornstein–Uhlenbeck stochastic volatility models

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  • José Fajardo

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Abstract

We find necessary and sufficient conditions for the market symmetry property, introduced by Fajardo and Mordecki (Quant Finance 6(3):219–227, 2006 ), to hold in the Ornstein–Uhlenbeck stochastic volatility model, henceforth OU–SV. In particular, we address the non-Gaussian OU–SV model proposed by Barndorff-Nielsen and Shephard (J R Stat Soc B 63(Part 2):167–241, 2001 ). Also, we prove the Bates’ rule for these models. Copyright Springer-Verlag 2014

Suggested Citation

  • José Fajardo, 2014. "Symmetry and Bates’ rule in Ornstein–Uhlenbeck stochastic volatility models," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 319-327, October.
  • Handle: RePEc:spr:decfin:v:37:y:2014:i:2:p:319-327
    DOI: 10.1007/s10203-012-0136-4
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    References listed on IDEAS

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    1. Albert N. Shiryaev & Jan Kallsen, 2002. "The cumulant process and Esscher's change of measure," Finance and Stochastics, Springer, vol. 6(4), pages 397-428.
    2. Bates, David S, 1991. " The Crash of '87: Was It Expected? The Evidence from Options Markets," Journal of Finance, American Finance Association, vol. 46(3), pages 1009-1044, July.
    3. Ernst Eberlein & Antonis Papapantoleon & Albert Shiryaev, 2008. "On the duality principle in option pricing: semimartingale setting," Finance and Stochastics, Springer, vol. 12(2), pages 265-292, April.
    4. José Fajardo & Ernesto Mordecki, 2014. "Skewness premium with Lévy processes," Quantitative Finance, Taylor & Francis Journals, vol. 14(9), pages 1619-1626, September.
    5. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    7. Friedrich Hubalek & Petra Posedel, 2011. "Joint analysis and estimation of stock prices and trading volume in Barndorff-Nielsen and Shephard stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 11(6), pages 917-932.
    8. Fajardo, José & Mordecki, Ernesto, 2010. "Market symmetry in time-changed Brownian models," Finance Research Letters, Elsevier, vol. 7(1), pages 53-59, March.
    9. Hubalek, Friedrich & Sgarra, Carlo, 2009. "On the Esscher transforms and other equivalent martingale measures for Barndorff-Nielsen and Shephard stochastic volatility models with jumps," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2137-2157, July.
    10. Michael Schmutz, 2011. "Semi-static hedging for certain Margrabe-type options with barriers," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 979-986.
    11. 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.
    12. JosE Fajardo & Ernesto Mordecki, 2006. "Symmetry and duality in Levy markets," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 219-227.
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    Cited by:

    1. Fajardo, José, 2015. "Barrier style contracts under Lévy processes: An alternative approach," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 179-187.

    More about this item

    Keywords

    Barndorff-Nielsen and Shephard Model; Symmetry; Bates’s rule; Ornstein–Uhlenbeck process; C52; G10;

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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