How to model dependence between (1-Factor Hull White simulated) Yield Curves?

Pricing interest rate swaps is done by using the OIS (EONIA/SONIA) curve for discounting and the EURIBOR / LIBOR curve to project future cash flows.

I have created a Hull and White object and the simulation of both curves independently is straight forward (See below). However, in this situation, there is no correlation between the simulated paths. Solution would be to create dependence (correlation of typically 80%-90%) between the two Brownian Motions that generate the paths.

Any idea how this can be constructed within (or outside) the current framework? I cannot find any useful information in the documentation or anywhere else.

CHW1EURIBOR = HullWhite1F(SEURIBORRateSpec,dAlpha,dSigma);

CHW1OIS = HullWhite1F(SOISRateSpec,dAlpha,dSigma);

%%Simulate Scenarios

% For each scenario, we simulate the future interest rate curve at each

% valuation date using the HW one-factor interest rate model.

% Use reproducible random number generator (vary the seed to produce
% different random scenarios).

SPrevRNG = rng(0, 'twister');

dDt = diff(yearfrac(iSettle,vSimulationDates,0));

iNumPeriods = numel(dDt);

mScenariosEURIBOR = CHW1EURIBOR.simTermStructs(iNumPeriods,...

      'nTrials',iNumScenarios,...

      'deltaTime',dDt);

mScenariosOIS = CHW1OIS.simTermStructs(iNumPeriods,...

      'nTrials',iNumScenarios,...

      'deltaTime',dDt);

% Restore random number generator state

rng(SPrevRNG);