  We propose a generic calibration framework to both vanilla and no-touch
options for a large class of continuous semi-martingale models. The method
builds upon the forward partial integro-differential equation (PIDE) derived in
Hambly et al. (2016), which allows fast computation of up-and-out call prices
for the complete set of strikes, barriers and maturities. It also utilises a
novel two-states particle method to estimate the Markovian projection of the
variance onto the spot and running maximum. We detail a step-by-step procedure
for a Heston-type local-stochastic volatility model with local vol-of-vol, as
well as two path-dependent volatility models where the local volatility
component depends on the running maximum. In numerical tests, we benchmark
these new models against standard models for a set of EURUSD market data, all
three models are seen to calibrate well within the market no-touch bid--ask.
