Computing the implied volatility in local and stochastic
volatility models
Henri Berestycki* (Ecole des Hautes Etudes en Sciences Sociales)
Abstract.
Determining the implied BlackScholes volatility for call or put options
in
local and stochastic volatility models is a challenging theoretical problem
as well as one of practical relevance, for instance in calibration issues.
I
present here a joint work with Jerome Busca and Igor Florent, in which
we
develop a PDE approach to directly compute this volatility. A nonlinear
parabolic equation is derived for the implied volatility. It reveals some
singular limits elucidating in particular the structure of implied
volatility near expiry. I will also present a recent joint work with Jerome
Busca where this approach is used to determine the implied volatility
of
long options.
