2014/10/27 by Antoine Jacquier, Patrick Roome, Jacquier, Antoine +1
Economics, Econometrics and Finance · Mathematics · #60F10 #91G60 #91G99 #FOS: Economics and business #FOS: Mathematics #Pricing of Securities (q-fin.PR) #Probability (math.PR) #math.PR #msc:60F10 #msc:91G60 #msc:91G99 #q-fin.PR
paper · pdf · doi:10.48550/arxiv.1410.7206
32 pages, 16 figures New Section 5 providing more (financial) intuitions
arxiv created 2015/08/28 · arxiv updated 2015/08/31
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.