2025/12/19 by José Enrique Figueroa-López, Figueroa-López, José E., Ruoting Gong +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60G51 60F99 60G40 91G20 #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #stochastic dynamics and bifurcation
paper · doi:10.48550/arxiv.2512.17791
openalex publication_date 2025/12/19 · openalex created_date 2025/12/23 · openalex updated_date 2026/07/28
In the present paper, we study the near-maturity (t→ T-) convergence rate of the optimal early-exercise price b(t) of an American put under an exponential Lévy model with a \it nonzero Brownian component. Two important settings, not previous covered in the literature, are considered. In the case that the optimal exercise price converges to the strike price (b(T-)=K), we contemplate models with negative jumps of unbounded variation (i.e., processes that exhibit high activity of negative jumps or sudden falls in asset prices). In the second case, when the optimal exercise price tend to a value lower than K, we consider infinite activity jumps (though still of bounded variations), extending existing results for models with finite jump activity (finitely many jumps in any finite interval). In both cases, we show that b(T-)-b(t) is of order √(T-t) with explicit constants proportionality. Furthermore, we also derive the second-order near-maturity expansion of the American put price around the critical price along a certain parabolic branch.