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

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  • Jaehyun Kim
  • Hyungbin Park

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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  • Jaehyun Kim & Hyungbin Park, 2026. "Quadratic G-BSDEs for bond pricing with endogenous short-rate feedback," Papers 2609.19094, arXiv.org.
    • Handle: RePEc:arx:papers:2609.19094
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    References listed on IDEAS

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    1. Larry G. Epstein & Shaolin Ji, 2013. "Ambiguous Volatility and Asset Pricing in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 26(7), pages 1740-1786.
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    3. Ben S. Bernanke & Michael Woodford, 1997. "Inflation forecasts and monetary policy," Proceedings, Federal Reserve Bank of Cleveland, pages 653-686.
    4. Vorbrink, Jörg, 2014. "Financial markets with volatility uncertainty," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 64-78.
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