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Soft Bond Game Options Valuation in Discrete Time Using a Fuzzy-Stochastic Approach

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Abstract

Bond game options are complex financial instruments that include the aspects of the risk (stochastic uncertainty) of a term structure of interest rates, option (flexibility) and interactivity (game). Forecasting uncertainty also comprises the vagueness (fuzzy uncertainty), often neglected. The fuzzy-stochastic models encompass both features. The paper objective is to develop and apply the fuzzy-stochastic soft bond game option model in discrete time. This model is based on normal fuzzy sets of the T-number type, the decomposition principle and \(\varepsilon{\text{-}}cuts\). The forward induction arbitrage-free method for the Ho–Lee calibration of interest rates, the binomial model and the two-person zero-sum games are used. An application example of the fuzzy-stochastic soft bond game option model from the buyer perspective based on the power triangle numbers for three variants of fuzziness is developed and computed. Inclusion of vagueness allows reflecting better valuation conditions and getting a more complex valuation picture. The developed model can adequately reflect valuation conditions and considers all aspects of the complex valuation problem of the bond game options, besides risk, flexibility, interactivity and vagueness.

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Acknowledgements

The paper is supported by the Grant Agency of the VSB-Technical University Ostrava SP2022/58, SP2021/57. This support is gratefully acknowledged.

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The research was funded by the VSB-Technical University Ostrava.

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Authors and Affiliations

  1. Department of Finance, Faculty of Economics, VSB - Technical University of Ostrava, Sokolska 33, 701 21, Ostrava 1, Czech Republic

    Zdeněk Zmeškal, Dana Dluhošová, Petr Gurný & Haochen Guo

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  1. Zdeněk Zmeškal
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Contributions

All authors contributed to the paper conception, methodology and formal analysis and investigation. The first draft of the manuscript was written by ZZ, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. Conceptualisation: ZZ, DD, PG and HG; Methodology: ZZ, DD, PG and HG; Software: ZZ; Writing—Original Draft: ZZ; Writing—Review & Editing: DD, PG, HG; Funding acquisition: DD; Formal analysis and investigation: ZZ, DD, PG, HG.

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Correspondence to Zdeněk Zmeškal.

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Zmeškal, Z., Dluhošová, D., Gurný, P. et al. Soft Bond Game Options Valuation in Discrete Time Using a Fuzzy-Stochastic Approach. Int. J. Fuzzy Syst. 24, 2215–2228 (2022). https://doi.org/10.1007/s40815-022-01258-3

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