IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1305.5963.html
   My bibliography  Save this paper

Note on multidimensional Breeden-Litzenberger representation for state price densities

Author

Listed:
  • Jarno Talponen
  • Lauri Viitasaari

Abstract

In this note, we consider European options of type $h(X^1_T, X^2_T,\ldots, X^n_T)$ depending on several underlying assets. We give a multidimensional version of the result of Breeden and Litzenberger \cite{Breeden} on the relation between derivatives of the call price and the risk-neutral density of the underlying asset. The pricing measure is assumed to be absolutely continuous with respect to the Lebesgue measure on the state space.

Suggested Citation

  • Jarno Talponen & Lauri Viitasaari, 2013. "Note on multidimensional Breeden-Litzenberger representation for state price densities," Papers 1305.5963, arXiv.org, revised Jan 2014.
    • Handle: RePEc:arx:papers:1305.5963
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1305.5963
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    2. Brown, Donald J & Ross, Stephen A, 1991. "Spanning, Valuation and Options," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 3-12, January.
    3. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    4. Bick, Avi, 1982. "Comments on the valuation of derivative assets," Journal of Financial Economics, Elsevier, vol. 10(3), pages 331-345, November.
    5. Avi Bick., 1982. "Comments on the Valuation of Derivative Assets," Research Program in Finance Working Papers 125, University of California at Berkeley.
    6. Jarrow, Robert A., 1986. "A characterization theorem for unique risk neutral probability measures," Economics Letters, Elsevier, vol. 22(1), pages 61-65.
    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. Hassane Abba Mallam & Diakarya Barro & Yameogo WendKouni & Bisso Saley, 2021. "Pricing multivariate european equity option using gaussian mixture distributions and evt-based copulas," Papers 2105.10599, arXiv.org.
    2. Carlo Marinelli, 2024. "On certain representations of pricing functionals," Annals of Finance, Springer, vol. 20(1), pages 91-127, March.
    3. Carlo Marinelli, 2021. "On certain representations of pricing functionals," Papers 2109.05564, arXiv.org.
    4. Jonathan Ansari & Eva Lütkebohmert & Ariel Neufeld & Julian Sester, 2024. "Improved robust price bounds for multi-asset derivatives under market-implied dependence information," Finance and Stochastics, Springer, vol. 28(4), pages 911-964, October.
    5. Jonathan Ansari & Eva Lutkebohmert & Ariel Neufeld & Julian Sester, 2022. "Improved Robust Price Bounds for Multi-Asset Derivatives under Market-Implied Dependence Information," Papers 2204.01071, arXiv.org, revised Sep 2023.

    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. Jarno Talponen, 2013. "Matching distributions: Asset pricing with density shape correction," Papers 1312.4227, arXiv.org, revised Mar 2018.
    2. Jarno Talponen & Lauri Viitasaari, 2014. "Multidimensional Breeden-Litzenberger representation for state price densities and static hedging," Papers 1401.6383, arXiv.org.
    3. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    4. Brown, Donald J & Ross, Stephen A, 1991. "Spanning, Valuation and Options," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 3-12, January.
    5. Jarno Talponen, 2014. "On volatility smile and an investment strategy with out-of-the-money calls," Papers 1410.1426, arXiv.org.
    6. McGoun, Elton G., 2003. "Finance models as metaphors," International Review of Financial Analysis, Elsevier, vol. 12(4), pages 421-433.
    7. Alexandre M. Baptista, 2005. "Options And Efficiency In Multidate Security Markets," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 569-587, October.
    8. repec:wyi:journl:002108 is not listed on IDEAS
    9. Dilip B. Madan & Frank Milne, 1994. "Contingent Claims Valued And Hedged By Pricing And Investing In A Basis," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 223-245, July.
    10. Gianluca Cassese, 2017. "Asset pricing in an imperfect world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(3), pages 539-570, October.
    11. Galvani, Valentina, 2007. "A note on spanning with options," Mathematical Social Sciences, Elsevier, vol. 54(1), pages 106-114, July.
    12. Andrew Papanicolaou, 2021. "Extreme-Strike Comparisons and Structural Bounds for SPX and VIX Options," Papers 2101.00299, arXiv.org, revised Mar 2021.
    13. Jarno Talponen & Minna Turunen, 2022. "Option pricing: a yet simpler approach," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 57-81, June.
    14. Tsetsekos, George & Varangis, Panos, 1998. "The structure of derivatives exchanges : lessons from developed and emerging markets," Policy Research Working Paper Series 1887, The World Bank.
    15. Galvani, Valentina, 2009. "Option spanning with exogenous information structure," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 73-79, January.
    16. Zongwu Cai & Yongmiao Hong, 2013. "Some Recent Developments in Nonparametric Finance," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    17. Alexandre Baptista, 2000. "Options and Efficiency in Multiperiod Security Markets," Econometric Society World Congress 2000 Contributed Papers 0299, Econometric Society.
    18. Geert Bekaert & Robert J. Hodrick, 2001. "Expectations Hypotheses Tests," Journal of Finance, American Finance Association, vol. 56(4), pages 1357-1394, August.
    19. Thomas Kokholm & Martin Stisen, 2015. "Joint pricing of VIX and SPX options with stochastic volatility and jump models," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 16(1), pages 27-48, January.
    20. Nakashima, Kiyotaka & Ogawa, Toshiaki, 2020. "The Impacts of Strengthening Regulatory Surveillance on Bank Behavior: A Dynamic Analysis from Incomplete to Complete Enforcement of Capital Regulation in Microprudential Policy," MPRA Paper 99938, University Library of Munich, Germany.
    21. Król, Michał, 2012. "Product differentiation decisions under ambiguous consumer demand and pessimistic expectations," International Journal of Industrial Organization, Elsevier, vol. 30(6), pages 593-604.

    More about this item

    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:arx:papers:1305.5963. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.