Large-Time Asymptotics of the Heston Model: From IG to NIG

2010 ◽  
Author(s):  
Shu Tong Tse
Keyword(s):  
Large Time ◽  
Heston Model ◽  
Large Time Asymptotics ◽  
Time Asymptotics

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

2013 ◽  
Vol 16 (08) ◽  
pp. 1350047 ◽  
Author(s):  
MARTIN FORDE ◽  
ANDREY POGUDIN
Keyword(s):  
Implied Volatility ◽  
Large Time ◽  
Heston Model ◽  
Large Time Asymptotics ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Time Estimates ◽  
Time Asymptotics ◽  
Sabr Model

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 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).

SIMULATIONS OF THE LIFSHITZ–SLYOZOV EQUATIONS: THE ROLE OF COAGULATION TERMS IN THE ASYMPTOTIC BEHAVIOR

2013 ◽  
Vol 23 (07) ◽  
pp. 1177-1215 ◽  
Author(s):  
THIERRY GOUDON ◽  
FRÉDÉRIC LAGOUTIÈRE ◽  
LÉON MATAR TINE
Keyword(s):  
Asymptotic Behavior ◽  
Large Time ◽  
Finite Volume Schemes ◽  
Large Time Asymptotics ◽  
Asymptotic Profile ◽  
Time Asymptotics ◽  
Supersaturated Solid Solutions ◽  
Kinetics Of ◽  
Selection Of

We consider the Lifshitz–Slyozov system that describes the kinetics of precipitation from supersaturated solid solutions. We design specific Finite Volume schemes and we investigate numerically the behavior of the solutions, in particular the large time asymptotics. Our purpose is two-fold: first, we introduce an adapted scheme based on downwinding techniques in order to reduce the numerical diffusion; second, we discuss the influence of coagulation effects on the selection of the asymptotic profile.

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