Research article

Trajectorial asset models with operational assumptions

  • Received: 02 September 2019 Accepted: 06 November 2019 Published: 13 November 2019
  • JEL Codes: C61, C63, G11, G12, G13

  • The paper addresses the problem of providing a framework and an algorithm to evaluate super and sub replicating prices, for European options, having interesting risk-reward characteristics. A general operational framework is put forward and illustrated by an algorithmic construction of one-dimensional models for option pricing. Asset models are defined based on a class of investors characterized by how they operate on financial data leading to potential portfolio rebalances. Once observable variables are selected for modeling, necessary conditions constraining these variables and resulting from the operational setup are derived. Future uncertainty is then reflected in the construction of combinatorial trajectory spaces satisfying such constraints. As the risky asset unfolds, it can be tested dynamically for the validity of observable sufficient conditions that rigorously imply the validity of the models. The paper describes the resulting algorithmic construction of such trajectory spaces and, in the absence of probability assumptions, a minmax algorithm that is available to evaluate the super and sub replicating prices.

    Citation: Sebastian Ferrando, Andrew Fleck, Alfredo Gonzalez, Alexey Rubtsov. Trajectorial asset models with operational assumptions[J]. Quantitative Finance and Economics, 2019, 3(4): 661-708. doi: 10.3934/QFE.2019.4.661

    Related Papers:

  • The paper addresses the problem of providing a framework and an algorithm to evaluate super and sub replicating prices, for European options, having interesting risk-reward characteristics. A general operational framework is put forward and illustrated by an algorithmic construction of one-dimensional models for option pricing. Asset models are defined based on a class of investors characterized by how they operate on financial data leading to potential portfolio rebalances. Once observable variables are selected for modeling, necessary conditions constraining these variables and resulting from the operational setup are derived. Future uncertainty is then reflected in the construction of combinatorial trajectory spaces satisfying such constraints. As the risky asset unfolds, it can be tested dynamically for the validity of observable sufficient conditions that rigorously imply the validity of the models. The paper describes the resulting algorithmic construction of such trajectory spaces and, in the absence of probability assumptions, a minmax algorithm that is available to evaluate the super and sub replicating prices.


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    [1] Brigo D, Mercurio F (2006) Interest rate models-theory and practice: with smile, inflation and credit.
    [2] Britten-Jones M, Neuberger A (1996) Arbitrage pricing with incomplete markets. App Math Financ 3: 347-363. doi: 10.1080/13504869600000016
    [3] Campbell JY, Lo AW, MacKinlay CA, et al. (1997) The Econometrics of financial markets, Princeton, NJ: Princeton University Press.
    [4] Carassus L, Gobet E, Temam E (2006) A class of financial products and models where superreplication prices are explicit. Proceedings of the Ritsumeikan International Symposium on Stochastic Processes and Applications to Mathematical Finance, 67-84.
    [5] Carassus L, Vargiolu T (2018) Super-replication price: it can be ok. Esaim Proc Surv 64: 54-64.
    [6] Crisci D (2019) Trajectory based market models for two stocks. MSc. Thesis, Mathematics, Ryerson University.
    [7] Cutland NJ, Roux A (2012) Derivative pricing in discrete time.
    [8] Degano IL, Ferrando SE, González AL (2018) Trajectory based models. evaluation of minmax pricing bounds. Dyn Cont Discrete Impulsive Ser B Appl & Algorithms 25: 97-128.
    [9] Eberlein E, Jacod J (1997) On the range of option prices. Financ Stoch 1: 131-140.
    [10] Feng L, Li B, Podobnik B, et al. (2012) Linking agent-based models and stochastic models of financial markets. Proceedings of the National Academy of Sciences of the United States of America 109: 347-363.
    [11] Ferrando S, et al. (2019a) Appendix 1: Algorithm, trajectorial asset models in matlab. Supplementary material to: "Trajectorial Asset Models with Operational Assumptions".
    [12] Ferrando S, et al. (2019b) Appendix 2: Matlab software bundle implementing trajectorial models. file: Operational root.zip. Supplementary material to: "Trajectorial Asset Models with Operational Assumptions".
    [13] Ferrando SE, González AL, Degano IL, et al. (2019) Trajectorial market models: arbitrage and pricing intervals. Revista de la Unión Matemática Argentina 60: 149-185.
    [14] Föllmer H, Schied A (2013) Stochastic finance:an introduction in discrete time. third edition, 3.
    [15] Gilboa I (2009) Theory of decision under uncertainty.
    [16] Kahalé N (2017) Super-replication of financial derivatives via convex programming. Manage Sci 63: 2323-2339.
    [17] Merton R (1973) Theory of rational option pricing. Bell J Econ Manage Sci 4: 141-183.
    [18] Pfleiderer P (2014) Chameleons: the misuse of theoretical models in finance and economics. Revista de Econ Institucional 16: 23-60.
    [19] Rebonato R (2012) Volatility and correlation: The perfect hedger and the fox, second edition.
    [20] Schoutens W, Simons E, Tistaert J (2006) A perfect calibration! now what? Best Wilmott 2: 281-304.
    [21] Sniedovich M (2016) From statistical decision theory to robust optimization: A maximin perspective on robust decision-making, Robustness Analysis in Decision Aiding, Optimization and Analytics. Editors, M. Doumpos, C. Zopounidis and E. Grigoroudis., International Series in Operations Research & Management: 59-85.
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  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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