THE LARGE-MATURITY SMILE FOR THE SABR AND CEV-HESTON MODELS

摘要

Large-time asymptotics are established for the SABR model with β = 1, p ≤ 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 CEV-Heston model. Finally, we translate these results into a large-time estimates for implied volatility using the recent work of Gao and Lee (2011) and Tehranchi (2009).