IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2302.08838.html
   My bibliography  Save this paper

Measuring distribution risk in discrete models

Author

Listed:
  • Roberto Fontana
  • Patrizia Semeraro

Abstract

Model risk measures consequences of choosing a model in a class of possible alternatives. We find analytical and simulated bounds for payoff functions on classes of plausible alternatives of a given discrete model. We measure the impact of choosing a risk-neutral measure on convex derivative pricing in incomplete markets. We find analytical bounds for prices of European and American options in the class of all risk-neutral measures, and we also find simulated bounds for given classes of perturbations of the minimal martingale equivalent measure.

Suggested Citation

  • Roberto Fontana & Patrizia Semeraro, 2023. "Measuring distribution risk in discrete models," Papers 2302.08838, arXiv.org.
  • Handle: RePEc:arx:papers:2302.08838
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2302.08838
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ernst Eberlein & Jean Jacod, 1997. "On the range of options prices (*)," Finance and Stochastics, Springer, vol. 1(2), pages 131-140.
    2. Thomas Breuer & Imre Csiszár, 2016. "Measuring Distribution Model Risk," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 395-411, April.
    3. Margherita Doria & Elisa Luciano & Patrizia Semeraro, 2022. "Machine learning techniques in joint default assessment," Papers 2205.01524, arXiv.org, revised Sep 2023.
    4. Fabio Bellini & Pablo Koch-Medina & Cosimo Munari & Gregor Svindland, 2018. "Law-invariant functionals on general spaces of random variables," Papers 1808.00821, arXiv.org, revised Jan 2021.
    5. Cyrus Seera Ssebugenyi & Ivivi Joseph Mwaniki & Virginie S. Konlack, 2013. "On the Minimal Entropy Martingale Measure and Multinomial Lattices with Cumulants," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(4), pages 359-379, September.
    6. Rama Cont, 2006. "Model Uncertainty And Its Impact On The Pricing Of Derivative Instruments," Mathematical Finance, Wiley Blackwell, vol. 16(3), pages 519-547, July.
    7. Bardia Kamrad & Peter Ritchken, 1991. "Multinomial Approximating Models for Options with k State Variables," Management Science, INFORMS, vol. 37(12), pages 1640-1652, December.
    8. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    9. Denuit, Michel & Vermandele, Catherine, 1998. "Optimal reinsurance and stop-loss order," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 229-233, 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. Ivivi J. Mwaniki, 2017. "On skewed, leptokurtic returns and pentanomial lattice option valuation via minimal entropy martingale measure," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1358894-135, January.
    2. Yu Feng, 2019. "Theory and Application of Model Risk Quantification," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2019.
    3. Donald J. Brown & Rustam Ibragimov, 2005. "Sign Tests for Dependent Observations and Bounds for Path-Dependent Options," Cowles Foundation Discussion Papers 1518, Cowles Foundation for Research in Economics, Yale University.
    4. 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.
    5. Pressacco, Flavio & Gaudenzi, Marcellino & Zanette, Antonino & Ziani, Laura, 2008. "New insights on testing the efficiency of methods of pricing and hedging American options," European Journal of Operational Research, Elsevier, vol. 185(1), pages 235-254, February.
    6. Andrea Beltratti & Paolo Colla, 2007. "A portfolio-based evaluation of affine term structure models," Annals of Operations Research, Springer, vol. 151(1), pages 193-222, April.
    7. Bing-Huei Lin & Mao-Wei Hung & Jr-Yan Wang & Ping-Da Wu, 2013. "A lattice model for option pricing under GARCH-jump processes," Review of Derivatives Research, Springer, vol. 16(3), pages 295-329, October.
    8. Henryk Gzyl & German Molina & Enrique ter Horst, 2009. "Assessment and propagation of input uncertainty in tree‐based option pricing models," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 275-308, May.
    9. Areski Cousin & Ibrahima Niang, 2014. "On the Range of Admissible Term-Structures," Working Papers hal-00968943, HAL.
    10. Cassimon, D. & Engelen, P.J. & Thomassen, L. & Van Wouwe, M., 2007. "Closed-form valuation of American call options on stocks paying multiple dividends," Finance Research Letters, Elsevier, vol. 4(1), pages 33-48, March.
    11. Chuang-Chang Chang & Jun-Biao Lin, 2010. "The valuation of multivariate contingent claims under transformed trinomial approaches," Review of Quantitative Finance and Accounting, Springer, vol. 34(1), pages 23-36, January.
    12. Ren-Raw Chen & Jeffrey Huang & William Huang & Robert Yu, 2021. "An Artificial Intelligence Approach to the Valuation of American-Style Derivatives: A Use of Particle Swarm Optimization," JRFM, MDPI, vol. 14(2), pages 1-22, February.
    13. Bardia Kamrad & Ricardo Ernst, 2001. "An Economic Model for Evaluating Mining and Manufacturing Ventures with Output Yield Uncertainty," Operations Research, INFORMS, vol. 49(5), pages 690-699, October.
    14. Babbs, Simon, 2000. "Binomial valuation of lookback options," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1499-1525, October.
    15. Mohammed Berkhouch & Fernanda Maria Müller & Ghizlane Lakhnati & Marcelo Brutti Righi, 2022. "Deviation-Based Model Risk Measures," Computational Economics, Springer;Society for Computational Economics, vol. 59(2), pages 527-547, February.
    16. Dangl, Thomas & Wirl, Franz, 2004. "Investment under uncertainty: calculating the value function when the Bellman equation cannot be solved analytically," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1437-1460, April.
    17. Dirk Sierag & Bernard Hanzon, 2018. "Pricing derivatives on multiple assets: recombining multinomial trees based on Pascal’s simplex," Annals of Operations Research, Springer, vol. 266(1), pages 101-127, July.
    18. Bowei Chen & Jun Wang, 2014. "A lattice framework for pricing display advertisement options with the stochastic volatility underlying model," Papers 1409.0697, arXiv.org, revised Dec 2015.
    19. Donald Brown & Rustam Ibragimov, 2005. "Sign Tests for Dependent Observations and Bounds for Path-Dependent Options," Yale School of Management Working Papers amz2581, Yale School of Management, revised 01 Jul 2005.
    20. Areski Cousin & Ibrahima Niang, 2014. "On the range of admissible term-structures," Papers 1404.0340, arXiv.org.

    More about this item

    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:arx:papers:2302.08838. 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.