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Is Dupire's equation defined when the T input (the expiration) is equal to 0 (the current time)?

If it's not, how would you determine an appropriate local volatility to use at that time when modelling stock price movements?

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  • $\begingroup$ Well, at time zero, the second derivative is a delta function, so you'll get zero. But then if you use something like a milstein scheme, your vol will be a mix with that at the next time step, so you don't get zero... $\endgroup$
    – will
    Dec 1 '16 at 22:05

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