This has two related questions -
How frequently do equity derivative traders re-mark the implied volatility surface -
(i) once a day (e.g. at start of trading day, or end-of-day), or
(ii) multiple times a day depending on market observability of the underlying vanilla options?
Given the implied vol surface has been marked, how frequently do large banks with large equity exotics books recalibrate the local volatility -
(i) once a day, compute the parametrized functional form (e.g. coefficients of a polynomial in S and t), and use the same through out the day for submitting quotes to clients. Essentially, while the undelying stock price would be the latest intra day value in the exchange, the local volatility functions will saved in a database and remain unaltered intra-day.
(ii) Or do they re-calibrate the local volatility again from the latest implied vol surface (as saved by traders in the database) for every trade.
How about intra-day risk management - when the portfolios are re-valued and greeks re-calculated, are all the local volatilities for multiple underliers re-calibrated from implied vols or are they only using a prior end-of-day calibration of local volatility functions.
My main concern is the computation time involved in calibrating local volatilities for a huge number of underliers, multiple times a day. Will it be computationally burdensome, in practice?