IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb649/sfb649dp2006-035.html
   My bibliography  Save this paper

Spectral calibration of exponential Lévy Models [2]

Author

Listed:
  • Belomestny, Denis
  • Reiß, Markus

Abstract

The calibration of financial models has become rather important topic in recent years mainly because of the need to price increasingly complex options in a consistent way. The choice of the underlying model is crucial for the good performance of any calibration procedure. Recent empirical evidences suggest that more complex models taking into account such phenomenons as jumps in the stock prices, smiles in implied volatilities and so on should be considered. Among most popular such models are Levy ones which are on the one hand able to produce complex behavior of the stock time series including jumps, heavy tails and on other hand remain tractable with respect to option pricing. The work on calibration methods for financial models based on Lévy processes has mainly focused on certain parametrisations of the underlying Lévy process with the notable exception of Cont and Tankov (2004). Since the characteristic triplet of a Lévy process is a priori an infinite-dimensional object, the parametric approach is always exposed to the problem of misspecification, in particular when there is no inherent economic foundation of the parameters and they are only used to generate different shapes of possible jump distributions. In this work we propose and test a non-parametric calibration algorithm which is based on the inversion of the explicit pricing formula via Fourier transforms and a regularisation in the spectral domain. Using the Fast Fourier Transformation, the procedure is fast, easy to implement and yields good results in simulations in view of the severe ill-posedness of the underlying inverse problem.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Belomestny, Denis & Reiß, Markus, 2006. "Spectral calibration of exponential Lévy Models [2]," SFB 649 Discussion Papers 2006-035, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
  • Handle: RePEc:zbw:sfb649:sfb649dp2006-035
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/25126/1/513076395.PDF
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
    2. Susanne Emmer & Claudia Klüppelberg, 2004. "Optimal portfolios when stock prices follow an exponential Lévy process," Finance and Stochastics, Springer, vol. 8(1), pages 17-44, January.
    3. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    4. Rama Cont & Ekaterina Voltchkova, 2005. "Integro-differential equations for option prices in exponential Lévy models," Finance and Stochastics, Springer, vol. 9(3), pages 299-325, July.
    Full references (including those not matched with items on IDEAS)

    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. Belomestny, Denis & Reiß, Markus, 2006. "Spectral calibration of exponential Lévy Models [1]," SFB 649 Discussion Papers 2006-034, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    2. repec:hum:wpaper:sfb649dp2006-034 is not listed on IDEAS
    3. Ciprian Necula & Gabriel Drimus & Walter Farkas, 2019. "A general closed form option pricing formula," Review of Derivatives Research, Springer, vol. 22(1), pages 1-40, April.
    4. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
    5. Jose Cruz & Maria Grossinho & Daniel Sevcovic & Cyril Izuchukwu Udeani, 2022. "Linear and Nonlinear Partial Integro-Differential Equations arising from Finance," Papers 2207.11568, arXiv.org.
    6. Walter Farkas & Ludovic Mathys & Nikola Vasiljević, 2021. "Intra‐Horizon expected shortfall and risk structure in models with jumps," Mathematical Finance, Wiley Blackwell, vol. 31(2), pages 772-823, April.
    7. Cristian Homescu, 2011. "Implied Volatility Surface: Construction Methodologies and Characteristics," Papers 1107.1834, arXiv.org.
    8. Daniel Sevcovic & Cyril Izuchukwu Udeani, 2021. "Multidimensional linear and nonlinear partial integro-differential equation in Bessel potential spaces with applications in option pricing," Papers 2106.10498, arXiv.org.
    9. Daniel Ševčovič & Cyril Izuchukwu Udeani, 2021. "Multidimensional Linear and Nonlinear Partial Integro-Differential Equation in Bessel Potential Spaces with Applications in Option Pricing," Mathematics, MDPI, vol. 9(13), pages 1-12, June.
    10. Thomas Mazzoni, 2018. "Asymptotic Expansion of Risk-Neutral Pricing Density," IJFS, MDPI, vol. 6(1), pages 1-26, March.
    11. Ludovic Mathys, 2019. "On Extensions of the Barone-Adesi & Whaley Method to Price American-Type Options," Papers 1912.00454, arXiv.org.
    12. Hatem Ben-Ameur & Rim Chérif & Bruno Rémillard, 2016. "American-style options in jump-diffusion models: estimation and evaluation," Quantitative Finance, Taylor & Francis Journals, vol. 16(8), pages 1313-1324, August.
    13. René Carmona & Sergey Nadtochiy, 2012. "Tangent Lévy market models," Finance and Stochastics, Springer, vol. 16(1), pages 63-104, January.
    14. Ivanova, Vesela & Puigvert Gutiérrez, Josep Maria, 2014. "Interest rate forecasts, state price densities and risk premium from Euribor options," Journal of Banking & Finance, Elsevier, vol. 48(C), pages 210-223.
    15. Lukas Gonon & Christoph Schwab, 2021. "Deep ReLU network expression rates for option prices in high-dimensional, exponential Lévy models," Finance and Stochastics, Springer, vol. 25(4), pages 615-657, October.
    16. Viktor Stojkoski & Trifce Sandev & Lasko Basnarkov & Ljupco Kocarev & Ralf Metzler, 2020. "Generalised geometric Brownian motion: Theory and applications to option pricing," Papers 2011.00312, arXiv.org.
    17. Chendi Ni & Yuying Li & Peter A. Forsyth, 2023. "Neural Network Approach to Portfolio Optimization with Leverage Constraints:a Case Study on High Inflation Investment," Papers 2304.05297, arXiv.org, revised May 2023.
    18. Karl Friedrich Mina & Gerald H. L. Cheang & Carl Chiarella, 2015. "Approximate Hedging Of Options Under Jump-Diffusion Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-26.
    19. Kitsul, Yuriy & Wright, Jonathan H., 2013. "The economics of options-implied inflation probability density functions," Journal of Financial Economics, Elsevier, vol. 110(3), pages 696-711.
    20. H. Peter Boswijk & Roger J. A. Laeven & Evgenii Vladimirov, 2022. "Estimating Option Pricing Models Using a Characteristic Function-Based Linear State Space Representation," Papers 2210.06217, arXiv.org.
    21. Mr. Prakash Kannan & Mr. Selim A Elekdag, 2009. "Incorporating Market Information into the Construction of the Fan Chart," IMF Working Papers 2009/178, International Monetary Fund.

    More about this item

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:zbw:sfb649:sfb649dp2006-035. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/sohubde.html .

    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.