Local risk-minimization for exponential additive processes

Battle Count: 81

The paper is directly relevant to quantitative trading in the context of hedging derivatives in incomplete markets with non-stationary jump dynamics. The LRM strategy provides a theoretically optimal hedging ratio for option positions. However, the practical relevance is somewhat limited by: (1) the focus on a specific class of models (exponential additive without Gaussian component), (2) the mathematical complexity of implementation, and (3) the absence of transaction cost considerations or real market data validation. The time-dependent Lévy measure framework is relevant for modeling intraday patterns and regime-switching behavior in asset prices.

High implementation complexity due to: (1) the need to implement Malliavin-Skorohod calculus concepts for additive processes, (2) verification of six integrability conditions (A1)-(A6) on the time-dependent Lévy measure, (3) computation of the minimal martingale measure and its Radon-Nikodym density, (4) implementation of the Carr-Madan FFT method with proper damping parameter selection, (5) calculation of the cumulant generating function and its derivatives for the specific additive process, and (6) handling the time-dependence of the Lévy measure throughout all computations. The VGSSD process parameters and characteristic functions require careful numerical treatment.

The paper provides fully explicit mathematical formulas (Theorem 4.2, equations 4.8-4.11) and all numerical parameters (N=2^14, η=0.25, R=1.75, C=1, G=M, H=1/2, S_t=1, M∈{4,16}). However, no code repository or supplementary computational scripts are provided. The analytical derivations are self-contained, but reproducing the numerical experiments would require implementing the FFT-based Carr-Madan method and the specific Lévy density calculations for the VGSSD process independently.