IDEAS home Printed from https://ideas.repec.org/a/kap/revdev/v16y2013i1p25-52.html
   My bibliography  Save this article

The αVG model for multivariate asset pricing: calibration and extension

Author

Listed:
  • Florence Guillaume

Abstract

Luciano and Semeraro proposed a class of multivariate asset pricing models where the asset log-returns are modeled by a multivariate Brownian motion time-changed by a multivariate subordinator which consists of the weighted sum of a common and an idiosyncratic subordinator. In the original setting, Luciano and Semeraro imposed some constraints on the subordinator parameters such that the multivariate subordinator is of the same subordinator sub-class as its components, leading to asset log-returns of a particular Lévy type. This restriction leads to marginal characteristic functions which are independent on the common subordinator setting. In this paper, we propose to extend the original model by relaxing the constraints on the subordinator parameters, leading to marginal characteristic functions which become a function of the whole parameter set. Under this generalized version, the volatility of the log-returns depends on both the common and idiosyncratic subordinator settings, and not only on the idiosyncratic one, which makes the generalized model more in line with the empirical evidence of the presence of both an idiosyncratic and a common component in the business clock. For the numerical study, we compare the calibration fit of both univariate option surfaces and market implied correlations for a period extending from the 2nd of June 2008 until the 30th of October 2009 under the two model settings and assess the calibration risk arising from different calibration procedures by pricing traditional multivariate exotic options. In particular we show that the decoupling calibration procedure fails to accurately replicate the market dependence structure under the original model for highly correlated asset returns and we propose an alternative methodology which rests on a joint calibration of the univariate and the dependence structure and which leads to an accurate fit of the market reality under both the generalized and original models. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Florence Guillaume, 2013. "The αVG model for multivariate asset pricing: calibration and extension," Review of Derivatives Research, Springer, vol. 16(1), pages 25-52, April.
    • Handle: RePEc:kap:revdev:v:16:y:2013:i:1:p:25-52
    DOI: 10.1007/s11147-012-9080-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11147-012-9080-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11147-012-9080-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Harris, Lawrence, 1986. "Cross-Security Tests of the Mixture of Distributions Hypothesis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(1), pages 39-46, March.
    2. Elisa Luciano & Wim Schoutens, 2006. "A multivariate jump-driven financial asset model," Quantitative Finance, Taylor & Francis Journals, vol. 6(5), pages 385-402.
    3. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    4. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382, July.
    5. Lo, Andrew W & Wang, Jiang, 2000. "Trading Volume: Definitions, Data Analysis, and Implications of Portfolio Theory," Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 257-300.
    6. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    7. Patrizia Semeraro, 2006. "A Multivariate Time-Changed Lévy Model for Financial Applications," ICER Working Papers - Applied Mathematics Series 10-2006, ICER - International Centre for Economic Research.
    8. Dilip Madan, 2011. "Joint risk-neutral laws and hedging," IISE Transactions, Taylor & Francis Journals, vol. 43(12), pages 840-850.
    9. Laura Ballotta & Efrem Bonfiglioli, 2016. "Multivariate asset models using Lévy processes and applications," The European Journal of Finance, Taylor & Francis Journals, vol. 22(13), pages 1320-1350, October.
    10. Patrizia Semeraro, 2008. "A Multivariate Variance Gamma Model For Financial Applications," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-18.
    11. Vasiliki D. Skintzi & Apostolos‐Paul N. Refenes, 2005. "Implied correlation index: A new measure of diversification," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 25(2), pages 171-197, February.
    12. Reiichiro Kawai, 2009. "A multivariate Levy process model with linear correlation," Quantitative Finance, Taylor & Francis Journals, vol. 9(5), pages 597-606.
    13. Richard Finlay & Eugene Seneta, 2008. "Option Pricing With Vg–Like Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(08), pages 943-955.
    14. repec:dau:papers:123456789/1392 is not listed on IDEAS
    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. Gian Luca Tassinari & Michele Leonardo Bianchi, 2014. "Calibrating The Smile With Multivariate Time-Changed Brownian Motion And The Esscher Transform," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1-34.
    2. Boris Buchmann & Benjamin Kaehler & Ross Maller & Alexander Szimayer, 2015. "Multivariate Subordination using Generalised Gamma Convolutions with Applications to V.G. Processes and Option Pricing," Papers 1502.03901, arXiv.org, revised Oct 2016.
    3. Holger Fink & Stefan Mittnik, 2021. "Quanto Pricing beyond Black–Scholes," JRFM, MDPI, vol. 14(3), pages 1-27, March.
    4. Buchmann, Boris & Kaehler, Benjamin & Maller, Ross & Szimayer, Alexander, 2017. "Multivariate subordination using generalised Gamma convolutions with applications to Variance Gamma processes and option pricing," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2208-2242.
    5. Andrey Itkin & Alexander Lipton, 2014. "Efficient solution of structural default models with correlated jumps and mutual obligations," Papers 1408.6513, arXiv.org, revised Nov 2014.
    6. Hasan Fallahgoul & Gregoire Loeper, 2021. "Modelling tail risk with tempered stable distributions: an overview," Annals of Operations Research, Springer, vol. 299(1), pages 1253-1280, April.
    7. Lynn Boen & Florence Guillaume, 2020. "Towards a $$\Delta $$Δ-Gamma Sato multivariate model," Review of Derivatives Research, Springer, vol. 23(1), pages 1-39, April.
    8. Roman V. Ivanov, 2018. "Option Pricing In The Variance-Gamma Model Under The Drift Jump," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-19, June.
    9. Buchmann, Boris & Lu, Kevin W. & Madan, Dilip B., 2020. "Self-decomposability of weak variance generalised gamma convolutions," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 630-655.
    10. Roman Ivanov, 2015. "The distribution of the maximum of a variance gamma process and path-dependent option pricing," Finance and Stochastics, Springer, vol. 19(4), pages 979-993, October.
    11. Patrizia Semeraro, 2021. "Multivariate tempered stable additive subordination for financial models," Papers 2105.00844, arXiv.org, revised Sep 2021.
    12. Boris Buchmann & Kevin W. Lu & Dilip B. Madan, 2019. "Calibration for Weak Variance-Alpha-Gamma Processes," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1151-1164, December.
    13. Baule, Rainer & Shkel, David, 2021. "Model risk and model choice in the case of barrier options and bonus certificates," Journal of Banking & Finance, Elsevier, vol. 133(C).
    14. Ivanov Roman V., 2018. "On risk measuring in the variance-gamma model," Statistics & Risk Modeling, De Gruyter, vol. 35(1-2), pages 23-33, January.
    15. Hasan A. Fallahgoul & Young S. Kim & Frank J. Fabozzi & Jiho Park, 2019. "Quanto Option Pricing with Lévy Models," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 1279-1308, March.
    16. Florence Guillaume, 2018. "Multivariate Option Pricing Models With Lévy And Sato Vg Marginal Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-26, March.
    17. Boris Buchmann & Kevin W. Lu & Dilip B. Madan, 2018. "Calibration for Weak Variance-Alpha-Gamma Processes," Papers 1801.08852, arXiv.org, revised Jul 2018.
    18. Patrizia Semeraro, 2022. "Multivariate tempered stable additive subordination for financial models," Mathematics and Financial Economics, Springer, volume 16, number 3, October.
    19. Michele Leonardo Bianchi & Gian Luca Tassinari & Frank J. Fabozzi, 2016. "Riding With The Four Horsemen And The Multivariate Normal Tempered Stable Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-28, June.

    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. Petar Jevtic & Patrizia Semeraro, 2014. "A class of multivariate marked Poisson processes to model asset returns," Carlo Alberto Notebooks 351, Collegio Carlo Alberto.
    2. Florence Guillaume, 2018. "Multivariate Option Pricing Models With Lévy And Sato Vg Marginal Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-26, March.
    3. Boris Buchmann & Kevin W. Lu & Dilip B. Madan, 2018. "Calibration for Weak Variance-Alpha-Gamma Processes," Papers 1801.08852, arXiv.org, revised Jul 2018.
    4. Michele Leonardo Bianchi & Asmerilda Hitaj & Gian Luca Tassinari, 2020. "Multivariate non-Gaussian models for financial applications," Papers 2005.06390, arXiv.org.
    5. Petar Jevtić & Marina Marena & Patrizia Semeraro, 2019. "Multivariate Marked Poisson Processes And Market Related Multidimensional Information Flows," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 1-26, March.
    6. Elisa Luciano & Marina Marena & Patrizia Semeraro, 2013. "Dependence Calibration and Portfolio Fit with FactorBased Time Changes," Carlo Alberto Notebooks 307, Collegio Carlo Alberto, revised 2015.
    7. Lynn Boen & Florence Guillaume, 2020. "Towards a $$\Delta $$Δ-Gamma Sato multivariate model," Review of Derivatives Research, Springer, vol. 23(1), pages 1-39, April.
    8. Marina Marena & Andrea Romeo & Patrizia Semeraro, 2018. "Multivariate Factor-Based Processes With Sato Margins," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-30, February.
    9. Boris Buchmann & Benjamin Kaehler & Ross Maller & Alexander Szimayer, 2015. "Multivariate Subordination using Generalised Gamma Convolutions with Applications to V.G. Processes and Option Pricing," Papers 1502.03901, arXiv.org, revised Oct 2016.
    10. Boris Buchmann & Kevin W. Lu & Dilip B. Madan, 2019. "Calibration for Weak Variance-Alpha-Gamma Processes," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1151-1164, December.
    11. Marina Marena & Andrea Romeo & Patrizia Semeraro, 2015. "Pricing multivariate barrier reverse convertibles with factor-based subordinators," Carlo Alberto Notebooks 439, Collegio Carlo Alberto.
    12. Alexandre Petkovic, 2009. "Three essays on exotic option pricing, multivariate Lévy processes and linear aggregation of panel models," ULB Institutional Repository 2013/210357, ULB -- Universite Libre de Bruxelles.
    13. Roman V. Ivanov, 2018. "Option Pricing In The Variance-Gamma Model Under The Drift Jump," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-19, June.
    14. Buchmann, Boris & Kaehler, Benjamin & Maller, Ross & Szimayer, Alexander, 2017. "Multivariate subordination using generalised Gamma convolutions with applications to Variance Gamma processes and option pricing," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2208-2242.
    15. Martijn Pistorius & Johannes Stolte, 2012. "Fast computation of vanilla prices in time-changed models and implied volatilities using rational approximations," Papers 1203.6899, arXiv.org.
    16. Roman Ivanov, 2015. "The distribution of the maximum of a variance gamma process and path-dependent option pricing," Finance and Stochastics, Springer, vol. 19(4), pages 979-993, October.
    17. Feng-Tse Tsai, 2019. "Option Implied Stock Buy-Side and Sell-Side Market Depths," Risks, MDPI, vol. 7(4), pages 1-16, October.
    18. Erdinc Akyildirim & Alper A. Hekimoglu & Ahmet Sensoy & Frank J. Fabozzi, 2023. "Extending the Merton model with applications to credit value adjustment," Annals of Operations Research, Springer, vol. 326(1), pages 27-65, July.
    19. Matteo Gardini & Piergiacomo Sabino & Emanuela Sasso, 2020. "Correlating L\'evy processes with Self-Decomposability: Applications to Energy Markets," Papers 2004.04048, arXiv.org, revised Jul 2020.
    20. Stergios B. Fotopoulos & Venkata K. Jandhyala & Alex Paparas, 2021. "Some Properties of the Multivariate Generalized Hyperbolic Laws," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 187-205, February.

    More about this item

    Keywords

    Multivariate asset pricing; αVG model; Calibration; Calibration risk; G12; C63;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

    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:kap:revdev:v:16:y:2013:i:1:p:25-52. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.