In this research we investigate the impact of stochastic volatility on future initial margin (IM - a type of collateral) and margin value adjustment (MVA - the funding cost associated to posting collateral) calculations for interest rate derivatives. An analysis is performed under different market conditions, namely during the peak of the Covid-19 crisis when the markets were stressed and during Q4 of 2020 when volatilities were low. The Cheyette short-rate model is extended by adding a stochastic volatility component, which is calibrated to fit the EUR swaption volatility surfaces. We extend modern Fourier pricing techniques to accommodate RFR-rates (e.g. ESTR, SOFR) and derive closed-form sensitivity expressions, which are used to model IM profiles in a Monte Carlo simulation framework. The various results are compared to the deterministic volatility case. The results reveal that the inclusion of a stochastic volatility component can have a considerable impact on non-linear derivatives, especially for far out-of-the-money swaptions. The effect is particularly pronounced if the market exhibits a substantial skew or smile in the implied volatility curve. This can have severe consequences for funding cost valuation and risk management.