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@article{De:2017:10.1137/14098065X,
author = {De, Marco SDM and Hillairet, CH and Jacquier, A},
doi = {10.1137/14098065X},
journal = {SIAM Journal on Financial Mathematics},
pages = {709--737},
title = {Shapes of implied volatility with positive mass at zero},
url = {http://dx.doi.org/10.1137/14098065X},
volume = {8},
year = {2017}
}

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TY  - JOUR
AB  - We study the shapes of the implied volatility when the underlying distribution has an atom at zeroand analyse the impact of a mass at zero on at-the-money implied volatility and the overall level of thesmile.  We further show that the behaviour at small strikes is uniquely determined by the mass of theatom up to high asymptotic order, under mild assumptions on the remaining distribution on the positivereal line.  We investigate the structural di erence with the no-mass-at-zero case, showing how one can{theoretically{distinguish between mass at the origin and a heavy-left-tailed distribution. We numericallytest our model-free results in stochastic models with absorption at the boundary, such as the CEV process,and in jump-to-default models. Note that while Lee's moment formula [25] tells that implied variance is atmost asymptotically linear in log-strike, other celebrated results for exact smile asymptotics such as [3,17]do not apply in this setting{essentially due to the breakdown of Put-Call duality.
AU  - De,Marco SDM
AU  - Hillairet,CH
AU  - Jacquier,A
DO  - 10.1137/14098065X
EP  - 737
PY  - 2017///
SN  - 1945-497X
SP  - 709
TI  - Shapes of implied volatility with positive mass at zero
T2  - SIAM Journal on Financial Mathematics
UR  - http://dx.doi.org/10.1137/14098065X
UR  - http://arxiv.org/abs/1310.1020
UR  - http://hdl.handle.net/10044/1/48350
VL  - 8
ER  -

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