NEAR-MATURITY ASYMPTOTICS OF CRITICAL PRICES OF AMERICAN PUT OPTIONS UNDER EXPONENTIAL LÉVY MODELS

Battle Count: 100

The paper provides important theoretical foundations for understanding early exercise behavior of American put options near expiration under realistic jump-diffusion models. While not directly implementable as a trading strategy, the results inform: (1) numerical pricing algorithms for American options, (2) understanding when early exercise is optimal near expiration, (3) model calibration for Lévy-based pricing engines, and (4) risk management of American-style derivative positions. The convergence rates with explicit constants are particularly useful for practitioners implementing approximation schemes.

The paper involves highly advanced mathematical techniques including: Lévy process theory, variational inequalities in distributional sense, small-time large deviations, Itô-Meyer formula for semimartingales, local time analysis, comparison principles, and parabolic asymptotic expansions. The proofs span multiple sections with intricate estimates. Implementing the theoretical results numerically would require sophisticated stochastic calculus and PDE/IDE solvers. The mathematical sophistication is at the level of top-tier probability/finance journals.

The paper is purely theoretical with complete mathematical proofs provided in the main text and appendices. All assumptions are clearly stated (Assumptions 2.1, 2.3, 5.1). The results are analytical (convergence rates with explicit constants) rather than empirical, making them fully reproducible through verification of proofs. However, no numerical experiments or code are provided to validate the theoretical results computationally.