Paper #1458

Title:

On the second derivative of the at-the-money implied volatility in stochastic volatility models

Authors:

Elisa Alòs and Jorge A. León

Date:

November 2014 (Revised: July 2016)

Abstract:

In this paper we compute analytically the at-the-money second derivative of the implied volatility curve as a function of the strike price, for correlated stochastic volatility models. We obtain an expression for the short-time limit of this second derivative in terms of the first and second Malliavin derivatives of the volatility process and the correlation parameter.

Keywords:

Anticipating Itô's formula, Malliavin calculus, Hull and White formula, stochastic volatility models

JEL codes:

AMS subject classification: 91G99

Area of Research:

Statistics, Econometrics and Quantitative Methods

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