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