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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
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    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)

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