Asymptotic Separability of Diffusion and Jump Components in High-Frequency CIR and CKLS Models

Battle Count: 71

The paper is moderately relevant to quantitative trading. It provides a theoretically rigorous method for detecting jumps in interest rate and volatility processes, which is critical for risk management, derivative pricing, and strategy development. The CKLS/CIR models are directly applicable to short-rate modeling used in fixed-income trading. However, the paper is primarily theoretical/statistical rather than directly implementing a trading strategy. The robust jump detection could improve model calibration for options pricing, hedging, and regime-aware trading systems. The high-frequency asymptotic framework aligns with modern market microstructure data.

Implementation requires: (1) Euler-Maruyama discretization of the CKLS SDE, (2) numerical optimization of the density power divergence objective (non-standard loss function), (3) computation of standardized residuals, (4) extreme-value threshold calibration using Gumbel quantiles, (5) careful handling of the positivity constraint on X_t and the boundary at zero. The MDPDE objective involves numerical integration of the model-implied density. The theoretical framework is sophisticated, combining SDE theory, robust statistics, and extreme value theory. However, the core algorithm (estimate → normalize → threshold) is conceptually straightforward once the components are implemented.

The paper provides detailed simulation parameters (Eq. 14), explicit formulas for estimators, thresholds, and test statistics. All theoretical results are stated with proofs in the Appendix. However, no code repository or software implementation is mentioned. The simulation design is fully specified (sample sizes, jump parameters, diffusion parameters, sampling interval), enabling replication. The MDPDE objective function and normalized statistic are explicitly defined.