Short-Rate-Dependent Volatility Models

Battle Count: 162

The paper is primarily a theoretical/mathematical finance contribution focused on European option pricing under a novel class of stochastic volatility models linked to interest rates. It is relevant to quantitative trading in the context of derivatives pricing, volatility surface modeling, and understanding the link between monetary policy and equity volatility. However, it does not directly propose trading strategies, backtests, or empirical performance evaluations. The explicit pricing formulas could be implemented in trading systems for options valuation and risk management.

Implementation requires: (1) evaluating complex-valued special functions (confluent hypergeometric 1F1 for CIR, infinite series of Gamma functions, 3F2 hypergeometric functions, and Jacobi polynomials with complex indices for Jacobi), (2) numerical Fourier inversion along a carefully chosen contour in the complex plane, (3) root-finding for implied volatility, and (4) handling branch cuts and admissibility conditions for the complex parameters. The Jacobi model is particularly complex due to the infinite series with complex indices. The provided Mathematica code reduces practical difficulty but porting to other languages (Python, C++) would require careful handling of special functions.

The paper provides complete Wolfram Mathematica code in Appendices B.1 and B.2 for both the CIR-driven and Jacobi-driven models, including all parameter values, Fourier inversion, bond pricing, call pricing, and implied volatility computation. The mathematical derivations are fully self-contained with explicit formulas. However, no standalone code repository (e.g., GitHub) is provided, and the code is embedded in the PDF.