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Quadratic G-BSDEs for bond pricing with endogenous short-rate feedback

  • Jaehyun Kim
  • Hyungbin Park
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Abstract

We study robust bond valuation with endogenous short-rate feedback under volatility uncertainty. Within the G-expectation framework, the dependence of the short rate on the bond price yields a nonlinear fixed-point problem, represented by a quadratic G-BSDE for the logarithmic price. Under suitable assumptions, we establish existence, uniqueness, comparison, and stability for bounded finite-horizon solutions. An additional strict monotonicity condition yields a unique bounded infinite-horizon solution and exponential convergence of finite-horizon approximations on compact time intervals. We apply these results to inverse short-rate design, constructing discount-rate coefficients that reproduce admissible smooth bond-price targets at a fixed maturity. For long maturities, we construct feedback rules under which the compensated logarithmic price converges exponentially to a prescribed bounded state-dependent profile, while the asymptotic yield equals a specified target.

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Cite

BibTeXRIS
BibTeX
@misc{kim2026quadratic,
  title = {{Quadratic G-BSDEs for bond pricing with endogenous short-rate feedback}},
  author = {Jaehyun Kim and Hyungbin Park},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19094},
  eprint = {2609.19094},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19094},
}
RIS
TY  - UNPB
TI  - Quadratic G-BSDEs for bond pricing with endogenous short-rate feedback
AU  - Jaehyun Kim
AU  - Hyungbin Park
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.19094
UR  - https://arxiv.org/abs/2609.19094
AB  - We study robust bond valuation with endogenous short-rate feedback under volatility uncertainty. Within the G-expectation framework, the dependence of the short rate on the bond price yields a nonlinear fixed-point problem, represented by a quadratic G-BSDE for the logarithmic price. Under suitable assumptions, we establish existence, uniqueness, comparison, and stability for bounded finite-horizon solutions. An additional strict monotonicity condition yields a unique bounded infinite-horizon solution and exponential convergence of finite-horizon approximations on compact time intervals. We apply these results to inverse short-rate design, constructing discount-rate coefficients that reproduce admissible smooth bond-price targets at a fixed maturity. For long maturities, we construct feedback rules under which the compensated logarithmic price converges exponentially to a prescribed bounded state-dependent profile, while the asymptotic yield equals a specified target.
ER  -