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Restrictive Clauses in Loan Contracts: A Sequential Stackelberg Game Interpretation

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Abstract

We propose a dynamic stochastic game model to assess the value of restrictive clauses in private loan contracts. Restrictive clauses are used by lenders to mitigate their credit risk, for instance, by linking the interest payments of the borrower to some observable performance measure. We show how the value of these clauses for the lender and the borrower corresponds to the solution of a feedback Stackelberg game in discrete time. We consider two instances of restrictive clauses that are commonly found in the syndicated loan market, namely safety covenants and performance pricing, and provide numerical illustrations using representative instances to compare their relative efficiency.

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Data Availability

No datasets were generated or analysed during the current study

Notes

  1. Note that raising the physical default barrier above the borrower’s current asset value is equivalent to forcing bankruptcy.

  2. Using an aggressive strategy results in an additional payoff increasing the immediate reward of the borrower.

  3. The lender can impose immediate bankruptcy by raising the physical default barrier above the borrower’s current asset value.

  4. Note that the equilibrium value for the follower using the PP1 schedule is lower than under SC. This is due to the fact that, since a piecewise constant schedule is suboptimal for the leader, one has to increase the interest rate significantly to yield the same value as SC to the leader, which is detrimental to the borrower.

  5. In scenario PP2, the borrower tends to use asset substitution when variations in spreads from one mode to the other are lower.

  6. However this is not a reliable metric for the efficiency of these scenarios in preventing asset substitution since it does not account for the probability of the asset value reaching these areas.

  7. Results corresponding to the performance pricing clause are qualitatively very similar.

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Acknowledgements

This work was supported by NSERC (Canada) grant number RGPIN-2020-05053.

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Authors and Affiliations

  1. HEC Montréal, Montreal, Canada

    Michèle Breton & Tiguéné Nabassaga

  2. BNP Paribas CIB, Montreal, Canada

    Tiguéné Nabassaga

Authors
  1. Michèle Breton
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  2. Tiguéné Nabassaga
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Contributions

M.B. and T.N. contributed equally to the conception of the work and to the writing and revision of the paper. T.N. created the software used in the work.

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Correspondence to Michèle Breton.

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Appendix

Appendix

Table 1 lists the base-case parameter values used in the numerical illustrations. Table 2 defines the performance schedule corresponding to Scenarios PP1 and PP2.

Table 2 Performance modes and corresponding interest rates
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Breton, M., Nabassaga, T. Restrictive Clauses in Loan Contracts: A Sequential Stackelberg Game Interpretation. Dyn Games Appl 15, 28–47 (2025). https://doi.org/10.1007/s13235-025-00626-6

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