Large-maturity regimes of the Heston forward smile

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• 作者：Antoine Jacquier ; ^{a.jacquier@imperial.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Patrick Roome ^{p.roome11@imperial.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：60F10 ; 91G99 ; 91G60
• 刊名：Stochastic Processes and their Applications
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：126
• 期：4
• 页码：1087-1123
• 全文大小：622 K

文摘

We provide a full characterisation of the large-maturity forward implied volatility smile in the Heston model. Although the leading decay is provided by a fairly classical large deviations behaviour, the algebraic expansion providing the higher-order terms highly depends on the parameters, and different powers of the maturity come into play. As a by-product of the analysis we provide new implied volatility asymptotics, both in the forward case and in the spot case, as well as extended SVI-type formulae. The proofs are based on extensions and refinements of sharp large deviations theory, in particular in cases where standard convexity arguments fail.