IDEAS home Printed from https://ideas.repec.org/a/gam/jjrfmx/v18y2025i1p30-d1565621.html
   My bibliography  Save this article

A Model-Free Lattice

Author

Listed:
  • Ren-Raw Chen

    (Gabelli School of Business, Fordham University, New York, NY 10019, USA
    College of Management, Chang-Gang University, Taoyaun 33302, Taiwan)

  • Pei-Lin Hsieh

    (Department of Finance, National Cheng-Chi University, Taipei City 11605, Taiwan)

  • Jeffrey Huang

    (FICC, SinoPack Bank, Taipei 104, Taiwan)

  • Hongbiao Zhao

    (School of Statistics and Management, Shanghai University of Finance and Economics (SUFE), Shanghai 200433, China)

Abstract

Predicting future price movements has always been one of the major topics in financial research, and there is no better method to predict the future prices of an asset than using its derivatives. In this paper, we propose a model-free lattice model that describes the complete price evolution of the underlying asset and simultaneously re-prices all of its European options. Given that such a lattice is consistent with market option prices, it must embed all necessary risk factors (e.g., random volatility, random interest rates, and jumps) and market restrictions (e.g., mean-reversion and liquidity) that are priced into the European options.

Suggested Citation

  • Ren-Raw Chen & Pei-Lin Hsieh & Jeffrey Huang & Hongbiao Zhao, 2025. "A Model-Free Lattice," JRFM, MDPI, vol. 18(1), pages 1-19, January.
  • Handle: RePEc:gam:jjrfmx:v:18:y:2025:i:1:p:30-:d:1565621
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1911-8074/18/1/30/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/1911-8074/18/1/30/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mark Britten‐Jones & Anthony Neuberger, 2000. "Option Prices, Implied Price Processes, and Stochastic Volatility," Journal of Finance, American Finance Association, vol. 55(2), pages 839-866, April.
    2. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
    3. 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.
    4. Horatio Cuesdeanu & Jens Carsten Jackwerth, 2018. "The pricing kernel puzzle: survey and outlook," Annals of Finance, Springer, vol. 14(3), pages 289-329, August.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. Wan-Ni Lai, 2014. "Comparison of methods to estimate option implied risk-neutral densities," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1839-1855, October.
    7. 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.
    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. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
    2. Peter Carr & Liuren Wu, 2014. "Static Hedging of Standard Options," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 3-46.
    3. Jobst, Andreas A., 2014. "Measuring systemic risk-adjusted liquidity (SRL)—A model approach," Journal of Banking & Finance, Elsevier, vol. 45(C), pages 270-287.
    4. Ricardo Crisóstomo, 2021. "Estimating real‐world probabilities: A forward‐looking behavioral framework," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(11), pages 1797-1823, November.
    5. Jarno Talponen, 2013. "Matching distributions: Asset pricing with density shape correction," Papers 1312.4227, arXiv.org, revised Mar 2018.
    6. Steven L. Heston & Alberto G. Rossi, 2017. "A Spanning Series Approach to Options," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 7(1), pages 2-42.
    7. 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.
    8. Sanjay K. Nawalkha & Xiaoyang Zhuo, 2020. "A Theory of Equivalent Expectation Measures for Contingent Claim Returns," Papers 2006.15312, arXiv.org, revised May 2022.
    9. Ana M. Monteiro & Antonio A. F. Santos, 2020. "Conditional risk-neutral density from option prices by local polynomial kernel smoothing with no-arbitrage constraints," Review of Derivatives Research, Springer, vol. 23(1), pages 41-61, April.
    10. Weiping Li & Su Chen, 2018. "The Early Exercise Premium In American Options By Using Nonparametric Regressions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 1-29, November.
    11. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    12. Arindam Kundu & Sumit Kumar & Nutan Kumar Tomar, 2024. "A Semi-Closed Form Approximation of Arbitrage-Free Call Option Price Surface," Computational Economics, Springer;Society for Computational Economics, vol. 63(4), pages 1431-1457, April.
    13. Rompolis, Leonidas S., 2010. "Retrieving risk neutral densities from European option prices based on the principle of maximum entropy," Journal of Empirical Finance, Elsevier, vol. 17(5), pages 918-937, December.
    14. Beber, Alessandro & Breedon, Francis & Buraschi, Andrea, 2010. "Differences in beliefs and currency risk premiums," Journal of Financial Economics, Elsevier, vol. 98(3), pages 415-438, December.
    15. Johannes Ruf & Weiguan Wang, 2019. "Neural networks for option pricing and hedging: a literature review," Papers 1911.05620, arXiv.org, revised May 2020.
    16. Kyungsub Lee & Byoung Ki Seo, 2021. "Analytic formula for option margin with liquidity costs under dynamic delta hedging," Papers 2103.15302, arXiv.org.
    17. Elias Tzavalis & Shijun Wang, 2003. "Pricing American Options under Stochastic Volatility: A New Method Using Chebyshev Polynomials to Approximate the Early Exercise Boundary," Working Papers 488, Queen Mary University of London, School of Economics and Finance.
    18. Härdle Wolfgang Karl & Silyakova Elena, 2016. "Implied basket correlation dynamics," Statistics & Risk Modeling, De Gruyter, vol. 33(1-2), pages 1-20, September.
    19. repec:hum:wpaper:sfb649dp2010-021 is not listed on IDEAS
    20. Samuel N. Cohen & Christoph Reisinger & Sheng Wang, 2020. "Detecting and repairing arbitrage in traded option prices," Papers 2008.09454, arXiv.org.
    21. Bo Zhao & Stewart Hodges, 2013. "Parametric modeling of implied smile functions: a generalized SVI model," Review of Derivatives Research, Springer, vol. 16(1), pages 53-77, April.

    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:gam:jjrfmx:v:18:y:2025:i:1:p:30-:d:1565621. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.