For Risk Neutral simulation, an integrated curve needs to be specified and is interpreted as the average volatility at time . This is typically obtained from the corresponding ATM volatility. This is then used to construct a new variance curve which is defined as and for where are discrete points on the ATM volatility curve.

Points on the curve that imply a decrease in variance (i.e. ) are adjusted to . This curve is then used to construct instantaneous curves that are then input to the corresponding stochastic process.

The relationship between integrated and instantaneous curves where the instantaneous curves are defined on discrete points with is defined on by Simpson's rule:

and . Integrated curves are flat extrapolated and linearly interpolated.