Convergence of Heston to SVI

2010/02/18 by Gatheral, Jim, Jacquier, Antoine
#Computational Finance (q-fin.CP) #FOS: Economics and business #Pricing of Securities (q-fin.PR)

paper · doi:10.48550/arxiv.1002.3633

Abstract

In this short note, we prove by an appropriate change of variables that the SVI implied volatility parameterization presented in Gatheral's book and the large-time asymptotic of the Heston implied volatility agree algebraically, thus confirming a conjecture from Gatheral as well as providing a simpler expression for the asymptotic implied volatility in the Heston model. We show how this result can help in interpreting SVI parameters.

Related

• Large deviations for the extended Heston model: the large-time case
• Large-Maturity Regimes of the Heston Forward Smile
• On refined volatility smile expansion in the Heston model
• A note on essential smoothness in the Heston model
• Realized volatility and parametric estimation of Heston SDEs