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Skewness premium with L�vy processes

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  • Jos� Fajardo
  • Ernesto Mordecki

Abstract

We study the skewness premium (SK) introduced by Bates [ J. Finance , 1991, 46 (3), 1009-1044] in a general context using L�vy processes. Under a symmetry condition, Fajardo and Mordecki [ Quant. Finance , 2006, 6 (3), 219-227] obtained that SK is given by Bates' x % rule. In this paper, we study SK in the absence of that symmetry condition. More exactly, we derive sufficient conditions for the excess of SK to be positive or negative, in terms of the characteristic triplet of the L�vy process under a risk-neutral measure.

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  • Jos� Fajardo & Ernesto Mordecki, 2014. "Skewness premium with L�vy processes," Quantitative Finance, Taylor & Francis Journals, vol. 14(9), pages 1619-1626, September.
    • Handle: RePEc:taf:quantf:v:14:y:2014:i:9:p:1619-1626
    DOI: 10.1080/14697688.2011.618809
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    10. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
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    Cited by:

    1. José E. Figueroa-López & Sveinn Ólafsson, 2016. "Short-term asymptotics for the implied volatility skew under a stochastic volatility model with Lévy jumps," Finance and Stochastics, Springer, vol. 20(4), pages 973-1020, October.
    2. José Fajardo, 2018. "Barrier style contracts under Lévy processes once again," Annals of Finance, Springer, vol. 14(1), pages 93-103, February.
    3. Fajardo, José, 2015. "Barrier style contracts under Lévy processes: An alternative approach," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 179-187.
    4. José Fajardo, 2017. "A new factor to explain implied volatility smirk," Applied Economics, Taylor & Francis Journals, vol. 49(40), pages 4026-4034, August.
    5. Federico De Olivera & José Fajardo & Ernesto Mordecki, 2018. "Skewed Lévy Models And Implied Volatility Skew," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-16, March.
    6. 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.
    7. Jos'e E. Figueroa-L'opez & Sveinn 'Olafsson, 2015. "Short-time asymptotics for the implied volatility skew under a stochastic volatility model with L\'evy jumps," Papers 1502.02595, arXiv.org, revised Dec 2015.
    8. Fajardo, José, 2016. "Power Style Contracts Under Asymmetric Lévy Processes," MPRA Paper 71813, University Library of Munich, Germany.

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