Paper: arXiv 2609.19094

Authors: 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.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a highly theoretical and mathematically intensive framework for bond pricing under uncertainty. While it introduces novel concepts and extends existing G-BSDE theory, it lacks empirical validation or practical implementation details, focusing purely on theoretical existence and properties.

Research Flowchart

  flowchart TD
    A[Research Goal: Robust Bond Valuation with Endogenous Short-Rate Feedback under Volatility Uncertainty] --> B{Key Methodology: Quadratic G-BSDEs & G-expectation Framework};
    B --> C{Inputs: Short-Rate Feedback, Volatility Uncertainty, Bond Price Dynamics};
    C --> D[Computational Process: Fixed-point problem for logarithmic bond price];
    D --> E{Key Findings: Existence, Uniqueness, Comparison, Stability for Bounded Solutions};
    E --> F[Outcomes: Inverse Short-Rate Design, Asymptotic Yield Convergence, Exponential Convergence of Finite-Horizon Approx.];