From characteristic functions to implied volatility expansions
2015 ◽
Vol 47
(03)
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pp. 837-857
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Keyword(s):
For any strictly positive martingaleS= eXfor whichXhas a characteristic function, we provide an expansion for the implied volatility. This expansion is explicit in the sense that it involves no integrals, but only polynomials in the log-strike. We illustrate the versatility of our expansion by computing the approximate implied volatility smile in three well-known martingale models: one finite activity exponential Lévy model, Merton (1976), one infinite activity exponential Lévy model (variance gamma), and one stochastic volatility model, Heston (1993). Finally, we illustrate how our expansion can be used to perform a model-free calibration of the empirically observed implied volatility surface.
2015 ◽
Vol 47
(3)
◽
pp. 837-857
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2011 ◽
Vol 14
(04)
◽
pp. 433-463
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2020 ◽
pp. 1-33
2016 ◽
Vol 20
(4)
◽
pp. 973-1020
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Keyword(s):
2002 ◽
Vol 44
(3)
◽
pp. 319-335
◽
2016 ◽
Vol 19
(02)
◽
pp. 1650014
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2019 ◽
Vol 22
(04)
◽
pp. 1950009
2019 ◽
Vol 12
(4)
◽
pp. 159
◽