Paper: arXiv 2512.14662

Authors: Damir Filipović

Abstract

This paper develops a model-free framework for static fixed-income pricing and the replication of liability cash flows. We show that the absence of static arbitrage across a universe of fixed-income instruments is equivalent to the existence of a strictly positive discount curve that reproduces all observed market prices. We then study the replication and super-replication of liabilities and establish conditions ensuring the existence of least-cost super-replicating portfolios, including a rigorous interpretation of swap–repo replication within this static framework. The results provide a unified foundation for discount-curve construction and liability-driven investment, with direct relevance for economic capital assessment and regulatory practice.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous, axiomatic mathematical foundation for static fixed-income pricing, static arbitrage, and liability super-replication. However, it is purely theoretical without any empirical data analysis, backtesting, or real-world implementation scripts.

Research Flowchart

  flowchart TD
    A[Research Goal: Develop Model-Free Framework for Fixed-Income Pricing & Liability Replication] --> B[Inputs: Observed Market Prices & Liability Cash Flows]
    B --> C[Methodology: Static Arbitrage Theory & Convex Optimization]
    C --> D[Process: Construct Discount Curves & Solve Super-Replication Portfolios]
    D --> E[Outcome 1: Equivalence of No-Arbitrage & Positive Discount Curve]
    D --> F[Outcome 2: Least-Cost Super-Replicating Portfolios & Swap-Repo Framework]

Cited References (14)

  1. Stripping the S wiss discount curve using kernel ridge regression (2024) — link
  2. Stripping the Discount Curve—a Robust Machine Learning Approach (2025) — link
  3. Negative interest rate swap spreads signal pressure in government debt absorption (2024) — link
  4. The safety premium of safe assets (2021) — link
  5. Asset pricing (2001) — link
  6. The term structure of interbank risk (2013) — link
  7. Exact Smooth Term-Structure Estimation (2018)
  8. The U.S. Treasury yield curve: 1961 to the present (2007) — link
and 6 more
  1. Martingales and arbitrage in multiperiod securities markets (1979) — link
  2. Reconstructing the yield curve (2021) — link
  3. Parsimonious Modeling of Yield Curves (1987)
  4. Estimating and Interpreting Forward Interest Rates: Sweden 1992 - 1994 (1994) — link
  5. The T reasury– SOFR Swap Spread Puzzle Explained (2024) — link
  6. Noise as Information for Illiquidity (2013) — link

0 of 14 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.