Arbitrage-Free Pricing with Diffusion-Dependent Jumps

Battle Count: 79

Highly relevant for quantitative finance practitioners working on derivative pricing, risk management, and model calibration. The no-arbitrage condition provides a rigorous foundation for pricing under realistic jump-diffusion dynamics. However, the paper is purely theoretical without implementation guidance, numerical examples, or empirical validation, limiting immediate practical applicability. The framework is most relevant for quantitative researchers and model developers rather than direct trading strategy implementation.

The theoretical framework requires advanced knowledge of stochastic calculus, measure theory, Girsanov's theorem, and Esscher transforms. Implementation would require numerical integration of the no-arbitrage condition (Eq. 5.41), Monte Carlo simulation for pricing under the risk-neutral measure, and careful handling of the four jump types with their respective trigger conditions. The discrete-time structure simplifies implementation relative to continuous-time alternatives, but the multi-type jump structure adds complexity.

The paper provides complete mathematical proofs and derivations for all results. The theoretical framework is fully self-contained with explicit equations. However, it is purely theoretical with no numerical examples, code, or empirical validation provided. Reproduction requires advanced knowledge of stochastic calculus, measure theory, and mathematical finance.