Fixed-Income Pricing and the Replication of Liabilities

Battle Count: 86

The paper is primarily relevant to insurance asset-liability management and regulatory capital rather than active quantitative trading. However, the static arbitrage framework and discount-curve construction are foundational for fixed-income trading desks. The swap-repo replication insights are directly applicable to relative-value trading in government bonds and interest-rate swaps. The super-replication methodology could inform hedging strategies for structured products. The relevance is moderate: more aligned with ALM, risk management, and regulatory compliance than with high-frequency or directional trading strategies.

The theoretical framework is mathematically sophisticated (convex analysis, Farkas' lemma, Klee's separation theorem) but the core optimization problem is a standard linear program. Practical implementation requires: (1) constructing the cash-flow matrix C from market instruments, (2) defining liability cash-flow vector Z, (3) solving the LP min q^T P s.t. q^T C >= Z, and (4) encoding swap-repo strategies into the cash-flow framework. The main complexity lies in data preparation (mapping instruments to cash-flow grids, handling date misalignment via aggregation) and ensuring the no-arbitrage conditions hold. Standard LP solvers (e.g., simplex, interior-point) suffice for the optimization step.

The paper is fully theoretical with complete proofs provided in the Appendix. All theorems, definitions, and examples are self-contained and mathematically rigorous. No empirical data or code is required for verification. However, practical implementation would require market data (bond prices, swap rates, repo rates) and numerical LP solvers. The framework is deterministic and static, making it straightforward to reproduce the theoretical results.