The Impact of Stochastic Volatility on Initial Margin and MVA for Interest Rate Derivatives

ABSTRACT In this research we investigate the impact of stochastic volatility on future initial margin (IM) and margin valuation adjustment (MVA) 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 incorporate the latest risk-free rate benchmarks (RFR), which in certain markets have been selected to replace the IBOR index. We extend modern Fourier pricing techniques to accommodate the RFR benchmark 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 nonlinear 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.