Large-time asymptotics are established for the SABR model with β = 1, ρ ≤ 0 and β 1, ρ = 0. We also compute large-time asymptotics for the constant elasticity of variance (CEV) model in the large-time, fixed-strike regime and a new large-time, large-strike regime, and for the uncorrelated...

We derive a closed-form expression for the stock price density under the modified SABR model [see section 2.4 in Islah (2009)] with zero correlation, for β = 1 and β 1, using the known density for the Brownian exponential functional for μ = 0 given in Matsumoto and Yor (2005), and then...