“…PDE methods for continuous-time diffusions [9,32,51], large deviations [15,18], saddlepoint methods [20], Malliavin calculus [7,41] and differential geometry [26,33] are among the main methods used to tackle the small-maturity case. Extreme strike asymptotics arose with the seminal paper by Roger Lee [43] and have been further extended by Benaim and Friz [4,5] and in [30,31,23,15]. Comparatively, large-maturity asymptotics have only been studied in [55,19,36,35,21] using large deviations and saddlepoint methods.…”