IDEAS home Printed from https://ideas.repec.org/p/bbk/bbkefp/0602.html
   My bibliography  Save this paper

Option Pricing with Lévy-Stable Processes Generated by Lévy-Stable Integrated Variance

Author

Listed:
  • Alvaro Cartea

    (Department of Economics, Mathematics & Statistics, Birkbeck)

  • Sam Howison

Abstract

We show how to calculate European-style option prices when the log-stock price process follows a Levy-Stable process with index parameter 1 ≤ α ≤ 2 and skewness parameter -1 ≤ β ≤ 1. Key to our result is to model integrated variance [image omitted] as an increasing Levy-Stable process with continuous paths in T.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Alvaro Cartea & Sam Howison, 2006. "Option Pricing with Lévy-Stable Processes Generated by Lévy-Stable Integrated Variance," Birkbeck Working Papers in Economics and Finance 0602, Birkbeck, Department of Economics, Mathematics & Statistics.
    • Handle: RePEc:bbk:bbkefp:0602
    as

    Download full text from publisher

    File URL: https://eprints.bbk.ac.uk/id/eprint/26942
    File Function: First version, 2006
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-778, April.
    2. Yesim Tokat & Eduardo S. Schwartz, 2002. "The impact of fat tailed returns on asset allocation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(2), pages 165-185, May.
    3. Fama, Eugene F, 1971. "Risk, Return, and Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 79(1), pages 30-55, Jan.-Feb..
    4. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-777, April.
    5. Alvaro Cartea & Sam Howison, 2002. "Distinguished Limits of Levy-Stable Processes, and Applications to Option Pricing," OFRC Working Papers Series 2002mf04, Oxford Financial Research Centre.
    6. Elisa Nicolato & Emmanouil Venardos, 2003. "Option Pricing in Stochastic Volatility Models of the Ornstein‐Uhlenbeck type," Mathematical Finance, Wiley Blackwell, vol. 13(4), pages 445-466, October.
    7. Sergio Ortobelli & Isabella Huber & Eduardo Schwartz, 2002. "Portfolio selection with stable distributed returns," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(2), pages 265-300, May.
    8. Alan L. Lewis, 2001. "A Simple Option Formula for General Jump-Diffusion and other Exponential Levy Processes," Related articles explevy, Finance Press.
    9. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    10. Kraus, Alan & Litzenberger, Robert H, 1976. "Skewness Preference and the Valuation of Risk Assets," Journal of Finance, American Finance Association, vol. 31(4), pages 1085-1100, September.
    11. S. R. Hurst & Eckhard Platen & S. T. Rachev, 1999. "Option pricing for a logstable asset price model," Published Paper Series 1999-2, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, April.
    2. Álvaro Cartea, 2013. "Derivatives pricing with marked point processes using tick-by-tick data," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 111-123, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alvaro Cartea & Sam Howison, 2004. "Option Pricing with Levy-Stable Processes," OFRC Working Papers Series 2004mf01, Oxford Financial Research Centre.
    2. Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, April.
    3. Li, Minqiang, 2008. "Price Deviations of S&P 500 Index Options from the Black-Scholes Formula Follow a Simple Pattern," MPRA Paper 11530, University Library of Munich, Germany.
    4. J. Huston McCulloch, 2004. "The Risk-Neutral Measure and Option Pricing under Log-Stable Uncertainty using Romberg Fourier Inversion," Computing in Economics and Finance 2004 13, Society for Computational Economics.
    5. Chan, Tat Lung (Ron), 2019. "Efficient computation of european option prices and their sensitivities with the complex fourier series method," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    6. J. Huston McCulloch, 2003. "The Risk-Neutral Measure and Option Pricing under Log-Stable Uncertainty," Working Papers 03-07, Ohio State University, Department of Economics.
    7. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Finance and Stochastics, Springer, vol. 26(4), pages 733-769, October.
    8. Aït-Sahalia, Yacine & Li, Chenxu & Li, Chen Xu, 2021. "Closed-form implied volatility surfaces for stochastic volatility models with jumps," Journal of Econometrics, Elsevier, vol. 222(1), pages 364-392.
    9. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    10. Jean-Philippe Aguilar & Cyril Coste & Jan Korbel, 2016. "Non-Gaussian analytic option pricing: a closed formula for the L\'evy-stable model," Papers 1609.00987, arXiv.org, revised Nov 2017.
    11. Climent Hernández José Antonio & Venegas Martínez Francisco, 2013. "Valuación de opciones sobre subyacentes con rendimientos a-estables," Contaduría y Administración, Accounting and Management, vol. 58(4), pages 119-150, octubre-d.
    12. Giulia Di Nunno & Kk{e}stutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From constant to rough: A survey of continuous volatility modeling," Papers 2309.01033, arXiv.org, revised Sep 2023.
    13. Feng, Chengxiao & Tan, Jie & Jiang, Zhenyu & Chen, Shuang, 2020. "A generalized European option pricing model with risk management," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    14. Gonçalo Faria & João Correia-da-Silva, 2014. "A closed-form solution for options with ambiguity about stochastic volatility," Review of Derivatives Research, Springer, vol. 17(2), pages 125-159, July.
    15. Indranil Sengupta, 2016. "Generalized Bn–S Stochastic Volatility Model For Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-23, March.
    16. Jingzhi Huang & Liuren Wu, 2004. "Specification Analysis of Option Pricing Models Based on Time- Changed Levy Processes," Finance 0401002, University Library of Munich, Germany.
    17. Young Shin Kim & Kum-Hwan Roh & Raphael Douady, 2022. "Tempered stable processes with time-varying exponential tails," Quantitative Finance, Taylor & Francis Journals, vol. 22(3), pages 541-561, March.
    18. Carr, Peter & Wu, Liuren, 2007. "Stochastic skew in currency options," Journal of Financial Economics, Elsevier, vol. 86(1), pages 213-247, October.
    19. Ma, Chao & Ma, Qinghua & Yao, Haixiang & Hou, Tiancheng, 2018. "An accurate European option pricing model under Fractional Stable Process based on Feynman Path Integral," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 87-117.
    20. Borochin, Paul & Chang, Hao & Wu, Yangru, 2020. "The information content of the term structure of risk-neutral skewness," Journal of Empirical Finance, Elsevier, vol. 58(C), pages 247-274.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bbk:bbkefp:0602. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://www.bbk.ac.uk/departments/ems/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.